Bibliography of Schlicht Functions

S. D. Bernafdi A s \ o c i r r et ' ro l n s \ o ro l \ 4 a l h e n i a l i c( sR e r i r e d l .J.r i.rfl Lr,rcrsrl! ...

Author: S. D. Bernardi

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S. D. Bernafdi A s \ o c i r r et ' ro l n s \ o ro l \ 4 a l h e n i a l i c( sR e r i r e d l .J.r i.rfl

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BIBLIOCRAPHYOF SCHLICHTFUNCTIONS

1965) FART r ( PART U (1966-1975) , PAR.Trrr (1976-1981)

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CONTENTS

PAR]I(

'1965),,

PARI ll (1966 l9'15) l9ll I ) PART lll ( l9-76_

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CONTENTS

PARTt (

1965).

It (r966lr'r5) PARI'I l l ( 1 9 7 6 l 9 l j l )

lll 211

v1

BIBLIOGRAPHY OF

SCHLICHTzuNCTIONS -1e65) PARTI (

CONTENTS vii I

P:eface. BibliograPltY

Bibliography"" Supplementary

List of MathematicalJournals ' '

PaPers. ExpositorY T o p i cR e f e r e n c e. .3. . . . Co. recltons

" " '

l0r 113 116 117 I JL

PREFACE

tg'l-t o:::it;:,?li.:rl, T;; 1694references Thisbibliographvcontains

lTh*:l,f ::^:"""-"i"1*,:$L ;rm; H:t.*li. lil,**t"'"T'fr iilnu#f llrn,t*il";'ffi and ,ao.,r,r, Iecturenotes'

l*:'l*i'lill"iil'ili; ::i"#ru':'Ji:i::"+i,l*l;".xi::i::ifu ::iffi:*i*h*nui:I $i;;'i *"; t,TxJrff i{:i,::ilffi 'ror"uoo'"*imately the rematr 1400 papers' while ,nu,n' .

uo tiurioe'upt'v Tlfjii:l#;1::l;l':n::*:fi[:l:i]'i:' 'itiinttt or ll'lt"' titles the word univalent t'""i"t" oroximately736 of them

vlll

classof Horvever'*unl:"lttll]: irr the multivalent(or their equivalents) not specifically pJpt" *ttot"'fitle-s-,1ot and schlichtfunction' utt tontutntJ'in iunttiont'!o:*:1' tuntttons' are referto them,'utnu"vp"uifi-ttut theorems.in thesethreeclasses pu'f; rnuny ttut positive of funciions in the classof *tif ft"o*t' into theorems easilytransformed,a'sts

not ;rc lre '"1'::l'-:).:".n''h'."hle "n":::'lli::':,i trrebibriographv analvtic from tontuin

"tit:1;:t-lltt dealingpnmarilv*'itf' uniuatlntv' aremadeby nianywritersof sp"cific'references *nicn to iunctiontheory wereobtit'sunnorlingl references paperson schlichttunctron;'il;;; ii t:nltt-n]'.fl"ctionsand intainedfrom the UlUtrograpli"''tip"ptt' Bieberco"ifitlntt ' -fuUcr-p-olynomials' c'un'tyof treatments clude

i "JuirJ.i, l'",.: ::1,fi:T? ;*;l:li*r;,"$i;:#i.,'111, ;*' orsoruproperties rorms' ;ti'on,roepritz l?li'iilil'XilriiTiLlilffi ;;;;;' tion,nf theclifferential

"tti,+ritli"Ltf

rl.tttlrXli'jll orthogonaltraJectorres' ,i.ti""ii"., tott"ricalderivative' theory tt"ier who is f amiliarwith the quadraticdif ferentialib'rnt ift" ' toplcs of these therele''r-ancy recognize '""dily *'rr functions alent of unir. in the iitriogtuptty [52J]appeared Thc earliestpupt' ri'*tiln"rtt *"the l"r, 1965(withthesingie latest the o";.rr;;;.";.; and 1902, vear * veart96o) Koebe'spaper[688]' oi [i ii] *iiich exception "o;;;;'i; givingthefirstactualresultln in 1907'rsgtntt"lt:]"*utaetias published functtons' of univalent ihe theor,r' in beenreviewed tttitjjt 'rtt bibliography papers flve' fur Mathematik ivlostoi the ;rr ttt" z*tialblatt the Nlathernatictlntu'"o (FM)' and rotittrtti'tt derMathematik (Zbl) or in the Jahrbuch"il;;; theendof each "ii'il'"t 'iti'-1"ii* ondpownu'n.ii) iherotume ::!:'^:!3!,.* reviewnumbers' " rsOrefcrences^lacking referenceof tnt upp'o*tiluteiy technical aslecturenotes,dissertations, mostof themmay oecrassifieri recemtoo or papersnot vetpublished' colloquiums' ;;;;;;.,;it"otrts, in the Reviews' iv puLtitt.,tfor inclusion followsthe tu.9 A "suppremen'^"';i;;;;;;li" of "^Trences "j someof the more recently a iist intiuJJ' uno bibhograpnv rnain

erero"uii'r"'rtit::^i.li::":;l;:lT :'"TTffi'.';..andtwentv-one, APProximatelYone years during the

Reviews prblished ences were locatedin 'nt''U"ttt' were hun'jred and forty-two references 1940-1964,volumes f-ZS' f*o le31-1953' in tr'" z""rariiatto"uri'ita d1nl:.:f:'vears Iocated lcca-'edin were eighty-one-refueilces volumts l-102' One n'"atta and 3l-63'

il;;;;;-t published theJahrbuch

tqoo-tsrr'volumes

IX

mathematical A volume-by-volumesearchwas made of twenty-two A list of public' journut, *t i.t are readil; availableio the American is contain functionswhich they itr.r. jou.nut, and the paperson schlicht 'vhich are devoted foffo*ing thi: is a list of erpository papers of "1r.". ; puri,o u generalsurvcvcf th: developmentof ihc thcJrv ;;;i1;;; univalentand p-valentfunctions' hove been The vorious resultsin the theory of schlichtfuncticns those into sixty-eighl topics.Eoch tttptcis followed by a list of -rlrjrrlnrrt clossified thol pertoining to inthe bibtiogrophy that contain information the in the topic. M,reover, tt the end of each reference ..bihliograpb' topics the indicaling nimbers enclosedin brackets are topic re.j'erences whichorediscussedin|hereference.Thefoirowingtwoexai',rplesillustratethe principal use of the bibliog:aphy' conjecExa,npieI . Reference[363]tists"A proof of the Bieberbach Schiffer' M' and Garabedian ture for the fourth coefficient," by P' R paper may be The notation MR 17-24 indicatesthat a review of this page24.The numbersin iound in the MathematicalReviews,volume 17, paper containsinformation U.u.f.." 19, 17, . . , 541indicatethat the Functions)'topic regardingtopic T9 (Meiomorphic Urrivalent(p-va^lent) Bounds for the iiz tco!fn.i.nt Bounds), . . . ' topic T54 (Coefficients Class(S)). funcironrple 2. The reader rvho is interestedin close-to-conver ll29' 282'656' ' ' Al43l tions rvill iind thit topic, T5. The references be found, respectiveindicatethat informatiorrregardingthis topic may T G Erzohi' W' tV, in tft. pape:sby e. Sietecldand Z' Le*andowski' bv the letj. suffridg.. Numbersin brackets.preceded ii;pi";, .'. . , r. indicatereferenceto the SupplementaryBibliography' Theclassificationoftheva;iouspirpersintotopicswasbasedona (of the full-length reading of approxirnately five hundred reprints (b'icl) abstractsor the of pup..rj, and in mosl caseson a reading we emphasizethat the i."i.*i. Therefore, in fairnessto the authors' of the papers' classificationsdo not inciicatethe completescope paperpublished It is difficult in a work of this natureto coverevery it is felt that this on the subject of schlicirt functions' However' the publicationsin this iitriogrupiti does include a major portion of field. the aid givenme by.n.rygraduatestudents I gratefullyacknowledge me !'"ilh someof the GeralJBierman and Victor Stanioniswho assisted ambiguousreferences' numeroustasks of filing, tracking down certian a n d t h e t r a n s l a t i o n o f s o m e f o r e i g n p a p e r s . T h e r e p l i e s t o m y take requests gratifying and I for renrints from numerousauthors were indeed

I owe many this opportunity to extend to them my heartfelt thanks. library thanksilso to the most cooperativepersonnelof the mathematics To New York Univerat the Courant Instituteof MathematicalSciences. and Science sity I am indebted for the financial aid given me by the Arts FinalResearchFund that helpedpay the cost of typing the manuscript. ly,Iwishtoexpressmysincereappreciationtothechairmanofmy graciouslyin clepartment,ProfessorF. A. Ficken, who cooperatedmost and convearianging my teachingscheduleso as to give me sufficient nientlntervalsof time to enableme to completethis bibliography' S. D. Bernardi May 1966

r

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS (PART I) J' GakugeiTokushimaUniv' l. Abe, H- A noteon subordinotion' MR 19-401'Ul Nat. Sci.Math 7(1956),47-51' d-omoin'Sugaku a ring-shaped 2. Abe, H. on conformalmannilslf 20-664P' 10' 18' 481 ,2s';;' tiupu"tttl MR 8(1956/s?) J' GakugeiTokushimaUniv' '3. Abe, H. On p-vaienifunctions' 16' 17' 19] 14' a(iqizl, 33-40.MR 20-i05' [9' in on annulus' Kodai Math 4. Abe, H. on 'o^'-oiotytic iunction' 1 0 ' l 3 ' 1 5 '4 8 ' 6 6 1 4 5R' 2 0 - 5 4 4 ' f 2 ' 6 ' S e mR ' e p .1 0 ( 1 9 5 8 ) , 3 8 - M in an urtnulus'Math' Japon' 5. Abe, H. On uniiitent functions 13',15', 17' 25' 2'7' 48' 58] , zs-ig. N',rnzi-zs3' l9', 5(1958/59) d'unefonctionholomorphe N' i)' rc cercled'univalence 6. Abramesco, deuxzerosd'une eqrntion petite distance,entre plus la sur (x) et f [43] 834-836'Zbr4-10' Sti' Paris194(1932)' .f (x) = /. C.R' ;tlO' holomorphe d-'une fonctio^n N' Surle cercled'univalence 7. Abramesco, d'une equation zeros cleux petite distanceentre f (x) et sur la pius Zbl 9-76' 49-s4' --l. Rt;;:"6i"' r'aut'Palermo58(1934)' f (x) t43l

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

zur Theorieder konformen Abbildung g. Ahlfors,L. (Jntersuchungen Sci' Fenn' A' l(1930)' No' 9 und der gonrcnFunktioien' ActaSoc' FM 56-984. [s9] Picard. c'R. g. Ahlfors, L. Su) une generalisationdu theoremede ' Acad. Sci. Paris lg4(f%D,245-246' Zbl3-407 l59l lemma.Trans.Amer. Math. 10. Ahlfors,L. An exteision'ofschwarz's 371 S o c . 4 3 ( 1 9 3 8 )3,5 9 - 3 6 4Z' b l l 8 - 4 1 0 ' U 9 ' Duke tr{ath' J' l4(194'l)' 11. Ahlfor s, L. BoundedAnatytic Functions. 1-ll. MR 9-24-[37'60] and extremalproblemson com12. Ahlfor s,L. Opei nieminn surfaces 24(1950)' 100-134' pact subregions. Comment' Math' Helvet' MRi2-90. [59i Notes' Oklahoma A'and 13. Ahlfor s, L. Conformal mopping' Lecture , 9 5 1 .[ 5 9 ] M. College1 14.Ahlfors,L.Developmentofthetheoryofconfcrmdlmappingand R i e m a n n s u r f a c e s t | t r o u g h a c e n t u r y . C o n t r i b u t i o n s ! o t h e tMR heoryof No' 30 (1953)'3-13' Riemannsurfaces.a.nn' of Math' Stud'' 1 4 - 1 0 5 0[.5 e ] York' lg53' 247' MR 14-85?' 15. Ahlfors, L. Complex Analysrs'New

t5el 16.Ahlfors,L,ExtremalProblemeinderfunktionenTheorle.Ann. N / i R\ 9 - 8 4 5 ' 1 2 4 ) A c a d . s c i . F e n n .S e r .A . I . N o . 2 4 9 1 ( 1 9 5 8 ) , 9 ' l'7AlJfors,L.;Beurling,A'Invariantsconformesetproblemesextremoux.DixiemeCo-ngresdesMath.scandlnaves'(1946),341-351.

MR e-23.[5e] l S . A h l f o r s , L ' ; B e u r l i n g , A . C o n f o ; . m o l i n v a r i g n t s . a n12-17l' dfunction. t59l Acra Math. g:itqso), l0l-129. MR theoreticnut-sets. Invarianls. constructicn and lg. Ahlfors, L.; Beurling, A. confoimol of a Symposium ; Applications of conlormal Maps, Proceedings Appl' Math' Ser' No' 18' 243-245.Nat. Bureau of Standards' W a s h . ,1 9 5 2 .N I R 1 4 - 8 6 1 '[ 5 9 ] 20.Ahlfors,L.iGrunsky,H.UberdieBlockscheKonstante.Math.Z. 42(1937\,o7t-673' FM 63-300' U9l theorem' Kodai Math Sern' 21. Aikaw a, 3. On extensionof Sciwarz's R e p . 1 9 5 2 ( 1 9 5 2 ) , 1 0 4 - 1 0M6R' l 5 - 2 1 0 ' [ 3 7 ] univalenceof regular func22. Aksentev,L. A. Sufficient conditlonsfor tions.rzu.vvss.uceu,..Zaved.Matematrka(1958),No.3(4)'3-7. (Russian)MR 26-278' [4] 2 3 . A k s c r r t ' e v , L . A . E l e m e n t c r y c r i t e r i a f o r u n i v u l e n cMaiemhtika eintermsof Ucebn', Zaved' boundory charocteristics'lzv' Vyss'

Zbl 96-55'l!'6:r0' 621 No. Oitr),3-8'(Russian) (1959),

24.Aksent,ev,L.A.Integralrepresentationsofunivalentfunctions,

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

3

(1959)'Nc' 4(i 1)' 3 8' (RusIzv. Vyss.Ucebn'Saved'Matematika 231 sian) MR 24A-37 ' 14, 16' ^, partial ---l:^t sums o,,nc /r of powerserrcs' of 25. Aksent'ev,L. ;' d''the'uniialence Izv.V yss.U ce un' At' ed' lviatem atikuit' qOO) ' No' 5( 18) ' 12-15'( R us 43) stnl fvfn 74A-153' 14' 20' 23' dani' (Jnivalentuoiio'ion of the pro{iie of s A. L. Aksent'ev, 26. ptoUlemam Teorii Funkcii Issledovanija po Souremen-ny* Gosvdarstv' Izdat'Fiz-Mat' ttt*tnnogo' 335-340' Kompleksnoro MR23A-52'[4] Lit.. l{oscow,1950'(Rusiian) 2 ? . A k s e n i ' e v , L ' l - ' - O n t n ' u n i v a Vyss' l e n c eZaved' o f t h eIviatematika s o l u t i o n o j(196!)' theinverse Izv' hydromechonics' of problem MR 25-611'[59].' -- ; ^ No.4(23),3-7' (Russran) for star-likeness bounds for coi"'exitycnti 2g. Aleksandrov,i.'n. on SSSR Nauk Akad' and regula' fn a iincte'Dokl' functionsuniuotnni 20-161' [6' 10' 11' l2]' MR go:-90s'(Russian) (N.S.)116(195;t, 2 g .A l e ksa n d ro v,|,.,A.Conditionsfor convexity' the'tnit circlc' univalentinoft|teimageregnn by functio" -zaved. mapping under "g'io'and (1958),No. 6(7),3-6' (Rustrtatematita u.Jun. Izv. V,uss. sian;Mn ?3A-731'[10' 12' 35] 3 0 .A l e ksa n cro v,|.A.onthestar - shopedchor ocler lfthemVyss. appi ngs of o,i' ,ntuotentin thecircle.Izv. a comainbyfunctionsregular MR (tgsg)'No' 4(ll)' 9-15' (Russian) Ucebn.zu"'a' iutematika

on of soyefunctionats definition of Domains A. r. ,,. T;t-T;fL", Issledovaniya rrgulorin a -cir.cle. o7iunctionsunivalent'ond" the class Kompleksnogo Funkcii Teorii po Sou"'ntnnyrn ero!f9111n [6' l0' '12'291 Peremennor;"i'*;tti"n) MR 22A(r)-965' and fi' f'ncti'onsunivalent V/rriationatiroiiemo A' I' Fiz' 32. Aleksandrov, AftuJ' Nauk Armjan' SSRSeT' star-shapedin the circle' rt"' Z--f9'-inutsian'Armenlansummary) Mat. Nauk 14(1961)'No' 4' MR25-426.[6, 1?,29,36] values ^ the functionol "of 33. AleksanO,ou,L' A' Boundary univalent if nobmgryh'(functions J : J(f, f,.f' ,7) on tn"to"q6iel17-3i' (Russian) MR 26-744' in a circle-iiuirst<' Mat' z'

v' Extremalpropertiesof star-like v' '4('l96ii,' Oernikov' A'; I. fiJ-3]rdrov, ,-. ' (Russian)MR 241-267 Z" Mat' mappings.'Si^Ui"ft' zs-izto.[2,6, 10,24'29'39'491 Mat. SbornikN'S' 26(68) (Jnivalent ioiorontt y. on E. 35. Alenicyn, (1 9 s0 ),5 7 -7 4.MR 11- 589'ul p-volentin'lh''meon' Mat' Sbornik 36. Alenicyn,Y' E' On functfoni 14'27'331

tz-agl'[e' N.s.27(6eii'iojzss'-zgo't'{ir

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

of univ'qlent 37. Alenicyn,Y. E. on the estimationof the coefficients functions.Mat.SbornikN'S'28(70)(1951)'401-406'i\IR13-610' ll7 , 45, 521 3 8 . A l e n i c y n , Y . E . o n u n i v a l e n t f u n c t i o n s i n m u t t i p l y c o n niUR ecteddomains.Dokl. Akad. Nauk sssR (N'S.) 102(1955),861-863' t7-25.122,3ll 39.Aienicyn,Y.E'.onunivalentfunctionsinmultiptl|Connecteddo. rnains.Mat.Sb.N.S.39(81)(1956),315_336.(Russian)\1R18-292.

, 2,601 u 5 ,1 9 2

of univalent and 40. Alenicyn, Y. E. A contributittn to the theory sssR (N'S') functions. Dokl. Akad. Nauk Bieberbach-Eitenberg 247-24g.(Russian)lviR l8-293' tl5 ' 26' 34' 491 109(1956), 4l.Alenicyn,Y.E.onfunctionswithoutCommonvaluesondtheouter Dokl. Akad. Nauk boundary of the rioinain of valueso1 a functicn. ) ,0 5 5 - 1 0 5 7M' R 2 0 - 6 & ' [ 1 5 ' 2 6 ' 1 4 ] s s s R ( N . s . ) 1 1 5 ( 1 9 5 71 42.Alenicyn,Y'F,.Ottfunctions,pithoutcommonvaluesgndtheouter |l/^at' Sb' N'S' boundary of the dlmain of volues of a function' ) R 2 0 - 1 0 7 4 '1 2 6 l 4 6 ( 8 8 )( 1 9 5 8 ) 3, 7 3 - 3 8 8 (' R u s s i a nM 43.Alenicyn,Y.E.Anextensionoftheprincipleofsubordinationto multiptyconnectedregions.Dokl.Akad.NaukSssRl26(1959)' 231-234'(Russian)MR 22A(l)-126' U' 371 anil''apo zl4. Aienicyn,Y. E. FUnctionswithOutcotnmon values.155lsflsr S o u r e m e n n y m P r o b l e m a m T e o r i i F u n c k c i i K o m p l e k s t960' nogoPeremenMR -Mat' Lit'' Moscos' nogo, 34-38.Gosodarstv'Izdat' Fix' 2 2 A ( l ) - 1 8 9 9[.2 6 , 3 4 ] 45.Alenicyn,Y.p'.So^'extremalpropertiesoffunctionsrnultiralent inmultipll'connecteddomoins'Dckl'Akad'NarrkSSSRl46(1962)' 60] 267-269.(Russian)MR 26-743' [14' 17' 27' 33' 46.Alenicyn,Y.E'ontherangesofsystemsofcoefficientsoffunctions representableasasumofstiettjesintegrals.VestnikLeningrad Univ'|7(1962),No.7,25_1|.(Russian.Englishsur-nmar})MR 2 5 - 4 2 6 . 1 21 , 3,23,291 4 7 . A l e n i c y n , Y . E . ; H a r ' i n s o n , S . Y . T h e r o d i u s o f p - v a l e n c e f o r(N'S') bounded Mat' Sb' domains. connected multiply in analyticfunctions 60i 52(94)(1960), 653-657.(Russian)MR 2zA(l)-,1628' [4j' 4S.Alenitzyn,G.onthecoefficientsofp.valentfunctions.Rec.Nlath. English sum(Mat. Sbornik)N.S. 10(52),lg42)' 51-58' (Russian' m a r Y )M R 4 - l 3 8 [ 1 4 , l : , 1 7, 5 0 , 6 5 1 4g.Alenitzyn,G.Onlhecoefficientsof,,schlicht''fuitctions.Rec. Math.(Mat.Sbornik)N'S'15(57)'(1944)'131-138'(Russian' 45' 52' 67] Englishsummary)MR 7-54') [15' 17' 39'

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCIILICHT

5

5 0 . A l e r , i r z y n , G ' O n t h e l o c a l l yrurs-r n i vji."eussian. alentfunctio n s ' ] e 1summarv) ''Math'(Mat' English

(1946), N.S.18(60), Sbornik)

Rec'Math'(N{at'Sborp'.'',1t"!t^'unctioiis' rneon xtlJ;;t ,,. MR 9-23'[27'33] unit nik)N.s. zo
e53) be'Ark'Mat'2(1 nsiunt orKoe o c h e rc ;t]) !1,' l' f: ,, . f;5]1,; -on-: or propertie-s extreme of some extension ;:?), ii-iti Len,- ff,"t;,l,JA Vestnik

fitt,,ctions. to no.n-Schiicht Schlichtfunctions in a ring Englishsummarv) (Russiarr'

rngraduniv' i;69;bt' NJ' rl

"7r-82'

de sur testransformees t$'tl Quetques.th|orDmes X.LSiti;tl: C' ,r. reeles' R' a" iinctions tlplly':unt

Fourieret sur lescoeffici'nt' 1?'5l' 36] su-sqi 'l/in rg-sis'-[6'13' Acad.Sci'Paris 2M(1g57)' de Taylorde certainesc/asses coeffirirlnu, lei Sur K. i. 56. Artemiadis, p"tit ZA+tfeSll'ltl-l l5' MR 19-22' defonction''C' n' Atad' Sci'

de M' s' d'un theoreme Gtndrotisation K' N' ,r. ll;,.k,131',

Mandelbroj,.'b.n.Acad'sj..'pu'i'24+(|957),834-836.MR

,r. f;lirt;ilri''u

etteurapptications deFourier iransform'ees K. sur tes jijrt*ent d'ordrep' Ann' sci'

reeles ,y ouxsericset sur les fonciion, zbl 89-53'U3l 269-318' 74. EcoleNorm' Sup'III' Ser' ti6!z)'inolyticf,tnctionin itscircleof )'ni oln' 5g. Arwin, A. rh;;o'rron intrgrot 48-395'[59] i $ -t'q1 - "* conversenc'' enn' M ath' 23' -d;;l-iz) of valu'e's of analyticfuncV: dn-"iioln 60. Ainevic,I' Ya; Ulina' G' ti o n sre p re sentedbyastiettj"' tni' s' a' VestnikLeningr adU ni v '

10(1955),*""iiii-qz'eui'iuni^imer'Math'Soc'Transr'Q)22'

- ,291 6' 13' 23' 1 ?- 59g' 12' Bull' 8 1 -9 4 MR . J'unctions' dr';;;;;es of univalent p. on H. fraction"t Arkins, 61. MR 8-326'll5' 421 q46)1060-1064' Amer. fufutt''Jot' SZtf konvexenkon62. Aumann, Georg' Die uit.tetiini*"""'ung'bei 80-82'MR 2-S3' [s9] tvtath'Z' +O(rq+o) formen An"oiii'i^'in' bei konvexenkonai' st)rri)-nver'zerrung 63. Aumann, Georg. IJber Akad' Wiss' 1948 s' -e' NIu't'' Nut' Ki' Baver' ealAiii"s' formcn ft4n t1- 507'U0' 291 ,' ..- :.,^tnntes 3 0 3 -308' (1 9 4 9 ), untvate' dansle ce r c l e localement les Satr fonctions R' Ballieu, 64. 4r3-4rs' zbr r8-r43' [15'68] 20;t;38t' Paris sci' Acad' uniteC.R'

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

65. Ballieu, R. szr tesfamilles defonctions localementunivolentesdans le cercleunite. Ann. Soc. Sci. Bruxelles,ser. L 58(1938),103-114. z b l 1 9 - 6 9 .[ 1 5 , 6 8 ] 66. Banach, S. sur leslignes rectificableset les surfacesdout I'oire est FM 5l-199' [591 finie. Fund. Math. 7(1925),225-236. 67. Basilewitsch, J., (Basilevitch) Zum Koeffizientenproblem der schlichten Funktionen. Mat. Sb. (Rec. Math.) (N. s.) l(1936), 2 l l - 2 3 6 . F M 6 2 - 3 7 2 .l r 7 , 4 9 1 68" Basilewitsch,.I., (Basilevitch)Sur lesth1orbmesde Koebe-Bieberbacli Rec.Math.Moscott.N.S.l(1936),283'291'Zbll5-71'[15,68] 59. Basilewitsch, J., (Basilevitch) sur la th|orie des fonctions univolentes.Rec. Math. Moscou N. S. 3(1938),359-366.(Russian) zbl 19-27l. U7 , 241 70. BasilewitschSar un th\orbme de Littlewood et Paley. Rec. Math. (Mat. Sbornik)N. s. 6(48),337-3M (1939).(Russian,Frenchsumm a r y )M R l - 3 0 8 . [ 1 5 , 1 7 , 4 5 , 5 2 , 6 7 1 71. Basilewitsch,J ., (Basilevitch) D'une propri|td extremalede la fonction f(a): z/(t -z)'. Rec. Math. (Mat. Sbornik) N' S' 12(54) ) R 5 - 2 5 9 '1 1 5 , 2 4 ' 3 9 ' (R (1943),315-319 . u s s i a nF. r e n c hs u m m a r y M 681 for the coefficients of 72. Biz\tevi6, I. E. Improvement of e-stimotes univalentfunctions 1. Mat. Sbonrik N. s. 22(64)(1948)381-390. M R 9 - 1 8 6 . [ 1 5 , 1 7 ,4 2 , 5 4 ] 73. Bazllevid, I- E. On distortiort theorents and the coefficients of univalentfunctions. Doklady Akad. Nauk sssR (N. S.) 65(1949)' 253-255.MR 10-602.19,15, 19, 42, 581 74. BazileviE, I.E. On distortion theorems for univalent functions. UspehiMatem.Nauk(N.S.)4No.3(31)(1949),128_130.MR I l - 5 0 8 . [ 9 , 1 5, 1 9 ,4 2 , 5 8 1 75. Bazilevi[, I. E. On distortion theoremsand coefficientsof univalent MR 12-600. func.ticns.Mar. Sbornik N. s. 28(70)(1951),i47-164. [ 9 , 1 5 , 1 7 , 1 8 , 1 9 , 2 4 , 4 2 , 4 5 ,5 4 , 5 8, 6 7 , 6 E ] 76. Bazilevid, I. E. On distortion theorems in the theory of univalent (Russian) functions. Mat. Sbornik N. s. 28(70), (1951), 233-292. M R i 3 - 6 4 0 . [ 9 , 1 5 ,2 4 , 5 8 , 6 8 ] 77. Bazilevid, I. E. On o cQSeof integrabitity in quadratures of the Loewner-Kufarevequution.Mat. Sb. N. S. 37(79)(1955),4',il-416. (Russian)MR l7-355. 14,6,24, 421 78. Bazilevid, I. E. Regions of the initiat coefficients of bounded univalent functions v;ith p-fotd symmetry. Mat. Sb. N. s. 43(85) (1957), 4Og-428.(Russia;r)MR 20-664. 122,U, 29, 491 79. Bazilevid.L E. On an estimute of the mean modulus in a clossof

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

1

Sb' (N' S') 48(90)(1959)' boundedunivalent functions'-Yu'' MR 22A(1)-795'13'19'22i qi-rca. (R'ussian) 80.Bazilevid,I.E.on,o*,propertiesofunivatentconformalmappings. (1954)iw-ztt' lY{R14-632'[6' 7' l0] Nrat.Sbornik.N. i' lzA+f curves G V' Certainpropertiesof level 8i. Bazilevid,I' E; foricttii' Dokl' tkld; Nauk' SSSR under univalentconformalnruppings' Doklady No' 5, 2(1961), Soviet"Math. 219-'280.(iussian); 149(1961)

i r g o - r t t i ti.u n 2 4 L - 3 7 0 ' 1 69' 7' l'o lpropertiesof

level curveson G' V' Stotrt€ 82. Bazilevid,I. E'; fo'itftii' univatentcon_fcrmcrmuJtpings.lr4at.Sb-(N.s.)58(1cc)(1952)' 7' 9' l0] 249-280.(Russian)MR 26-500' [6' 8 3 . B e a t t i ' , S . A n o t t ' o n s c h l i c h t f u n c t i oztil' n s '3"262' T r a n s127 ' R c' y421 'Soc'Canada

' III Math. s.i. iii s' zs(rvlrl' 83-85 of Schworz'Bull' Amer' lemma E' F' ; reiativeof the 84. Beckenbach, ' Zbl 19-350[59] Math' Soc.+a(tq38),698-?0-l Riesz'J' London q i' e" On theoremof Feier and 85. Beckenbach, 19-67' 159) lvlath.Soc.l3(1938)'82-E6' Zbl on analyticfuncof E' F' A property mean"!l-*: :! 86. Beckenbach, MR 14-629' (2) 1(1952)'15'l-163' lion. Rend'Circ' Mat' Palermo in co'nplex ;' w' on subordination ,r. H;J'."bach, E' F'; c-''aham' 211:25: Nat' Bureauof vqriabletheory' Proc' of a sympo'i"m' U'S' Govt'Print' Orfice' Appl' Math' Ser'(195j)No' 18 Standards .] , 6 , i 0 , 3 7 ] M R 1 4 - 6 3 2[-p' of Shniad'iH' On themeanmodulus 88. Beckenbach, f '; Gustin'W'; anonalyticfunction.Bull.n'*'.Math.Soc.55(i949),184-190. .rthecomplexdoM R i 0 - 4 4 1 .[ 3 ' 7 ] tn dis:cnjugacy and P. R' Nonoscitlation 89. Beesack, M R l8- 483'U4' A mer 'Math'sot' si( r q 56) ' 2ll- 242' ma i n .T ra n s. 3ll

. -.:^-^ ^nA r equationsa1l Y'onvexmopptngs' 90. Beesack,P'R' Linear differential 3l] r',rn zze(D-1629. [6, 10, 14, Duke Math. J.2i(1960), 483-495. of second B O; ii' z"ot'o7 solutions 91. Beesack,P' R'; Schwarz' canadian J. of Math' 8(1956)' order linear differentiat equotlo,nr. 5 0 4 - 5 1 5M . R l 8 - 2 1 1 '[ 3 1 ] g 2 . B e n d e r , J . S o m e e x t r e m g l t h e o r e m s f o r m u l t w a l e ' n t l y s t a14' r - l i15' kefunc24A-3?0' [6' MR 2g(lg62l'-tOt-tOO' tions.DukeMath' J' l ' 7, 2 3 , 3 6 , 5 0 , 6 3 , 6 5 ] 9 3 . B e l g , P ' W ' O n u n i v a l e n t m a p-ftu*' p i n g s b l s o l u tMath' i o n s oSoc' f l i n e84(1957)' orelliptir' Amer' partial differential equations'

-iaq i591 iro-rts. MR'18-74f Funktionen derharmonischen g4. Bergmunn,^s. dii E-ntwrcklung

B I B L I O G R A P H YO F S C H L I C H T F U N C T I O N S

der Ebene und des Raumes nach orthogonalfunktionen. Math. Ann. 86(1922),237-271. FM 48-1236.[59] 95. Bergmann,S. The kernelfunction and conformal mapping' Amer. , o . 5 , N e w Y o r k , 1 9 5 0 ,1 6 l p p ' M R t2-402. M a t h . S o c .S u r v e y sN

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96. bergmann, S.; Schiffer, M. M. Kernel functions and conformal mapping. Composito Math. 8(195l),205-249' MR 12-602' l59l R. 97. Bermant, A. Sir quetquesproperi\tds desfonctions r|guliDres.C. | 8 _ | 4 3. ( D o k l . )A c a d .S c i .U . R . S . S . ,N . S . l 8 ( 1 9 3 8 )|,3 7 _ | 4 o . Z b [ 6 , 1 8 ,1 9 ] A. Remarquesur le lemmede schwarz. c. R. Acad. Sci. Bermant, 98. 3l-33. Zbl 19-124.[6, 19, 37] (Paris)207(1938), 99. Bermant,A. Sur Ia variationde lo ditation d'unefonction reguliere. C.R.(Doklady)Acad.Sci.URSS(N.S.)45(|944)27|_273.MR 7 - 1 5 0 .[ 6 , l 9 ] 100. Bermant, A. Ditation d'une fonction modulaire et problemesde recouvrement.Rec. Math. (Mat. Sbornik) N. s. 15(57)(l9M)' 285-324.(Russian-Frenchsummary)MR 7-150' [l' 19] R. 101. Bermant, A. Cn a generalizationof Koebe's theorem. c. 8-202. h{R (Dokiaciy)Acad. Sci.URSS( N' S.) 52(1946),379-j8i.

tl el

principle 102. Bermant. A. On certqin generalizationsof E. Lindelof's and their applications.Rec. MatL^.(Mat. Sbornik) N. S. 20(62) ( 1 9 4 7 ) , 5 5 - 1 1M 2 .R 9 - 1 3 8 .I l ' 3 7 ] 103. Bernardi,S. D. T,.to theorentson schiichtfunctions. Duke Math. J . l 9 ( 1 9 5 2 ) , 5 - 2 1M. R i 3 - 7 3 3 .[ 1 7 ' 3 9 ] 104. Bernardi, S. D. A survey of the developmentof the theory of MR |4_35, Schtichtfunctions, Duke Math. J. 19(1952),263_287.

t44l

105. Bernardi, S. D. Note on Qn inequality of Prawitz. Duke Math. J.

2 3 (1 9 5 63),8 5 -3 9 1N. i R l 7- l 193.127,391 1Oti.Bernardi,S. D. Thecentroidof anolyticntappings'Arner. Math. MR 19-258'[49] Mon. 64(1957),259-26r.

107. Bernardi, S. D. A delerminontinequalityfor univalentfunctions' Amer.Math.Monthlv64(1957),495-497'MR19-539'U7'27'541 108. Bernardi,S. D. Rmcticns with positiverealpart and Schlichtfuncilons.DukeMath.J.26(1959),541-548'MR26-63'[2'4'6'l0l J' 109. Bernardi, S. D. Convex,starlike, and level curves' Duke Math 2 8 ( 1 9 6 1 )5, 7 - 7 2 .M R 2 3 A - 1 7 7. 1 6 ,1 0 , 1 3 , 3 5 1 110. Bernardi, s. D. circular regions covered b1' schlicht functions. MR 30-416' [19] Dukc Math. J. 32(19551,23"36. 111. Bernardi, S. D. Specia! classesof subordinatefunctions. Duke

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55, 67'[1' 6' l0' 13'20]' MR- 32- 992 l93Z' Ma th .J. 3 3 (1 966) A. s. Almost PeriodicFunctions.cambridge, 112.Besicovitch,

zbt 4-2s3.ls9l

J' Lon'lon Math' n. S' On two probleftlSo1rLowrer' ll3. Besicovitch, Soc. 27(1952),74t-l+4' MR 13-831'[59] Up'u'' un probleme de moioralion' Thesis' 114. Beurling, A. E;';'; sala, 1933.FM 59-1042'[59] wtd Praxis der konforrnenAbbildung' I 15. Bieberbach,L' Zur Theoiie Rc.CilcoloN{at'palermo3S(1914)'98-ll2'FM45-57 0'[59] y. 1ber einigetxlremtalproblcmeim cehieteder konBieberbacn, I16. 153-172.FM 46-549.19, ann. 77(t-916), rraurt-. formen aotitiuni. 19, 221 y' 0Oer aie Koeffizientem derieniger' Fotenzreihen' ll?. Bieberbach, w e l c h e e i n e s c h | i c h l e A b b i l d u n g d e s E i n h e i l s - k - r e46-552' isesvermitteln. [9' (tqtO)' 940-955'FM Sitzungsb' Wiss' Akad. Preuss.

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F M 4 7 - 3 2 7 .[ l c , 1 5 , 6 4 , 6 8 ] l1?.Bieberbach,L.NeuForschungenimGebieterlerkonformenAbbitdung.Glasnik.hrv'prirod'drustva'33(1921)'FM48-403'16'421 t,on nahen kreisformigen 120. Bieberbach,L'. 1be, die Kreisahbildung (1924)'181-188'FM Bereichen.Preuss'Akad' Wiss' Sitzungsber' 50-640.[19] l 2 l . B i e b e r b a c h , L . E i n e h i n r e i c h e n t t e B e d i n g u n g f u189-192' r s c h l i c hFM teAb' M' 157(1927)' F' J. ritskreises. nnt ai bildungen 53-372.[4, 15] Abbildungen. Bull' i. zW Theorie der schlichten Bieberbach, 122. FM 56-297' [19' 42' 43] Calcutta Math. Soc' 20(1928)'17-20' der konin_Gebiete 123. Bieberbach,y.\a.r riige Extremarprobleme Ann' 25(1935)'267-272'Il7 ' 491 formen Abbildung' Math' des Einheitskrei'ses 124. Bieberbach, 1". ffu'i tchlichte Abbildungeii durchmeromorpheFunktionen'||.S'-B.Preuss.Akad.Wiss. . b l 1 8 - 2 9 'U 9 l ( 1 9 3 7 ) 3, 5 9 - 3 6 5 Z l25.Bieberbach,L.LehrbuchderFunktionentheorie.V.2'2ndEdition.ChelseaPubl'Co',NewYork'1945'3'70'MR6-261't441 l26.Biebcrbach,L.ConformalMapping.CrreiseaCo.(TranslatedbyF. Stclnhardt),1953,234' Zbl 50-84' l44l Ergebnisse der r27. Bieberbach, t.' ,enatytischeiortsetzung. MathernatikundihrerGrenzgebiete.N.F.Heft3.Springer-Verlag, 1955'MR l6-913' [59] Berlin-Gottingen-Heidelberg' de fonctions 12g. Bielecki,e.; le*andowski, z. sur certainesfamitles

10

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

a-|toitdes.Ann. Univ. Mariae Curie-SklodowskaSect.A15(1961), 45-55. (Polish and Russiansummaries)MR 26-63.16l t 2 9 . Bielecki, A.; Lewandowski, Z. Sur un th|orime concernqntles fonctions univalentes lin^qirement accessiblesde M. Biernacki. M. R 2 6 - 9 8 0 .[ 5 ] A n n . P o l o n .M a t h . 1 2 ( 1 9 6 2 ) , 6 1 - 6 3 l 3 0 . Bielecki,A.; Lewandowski,Z. Sur une g,in,lralisationde quelques th\orbmes de M. Biernscki sur les fonctions analytiques. Ann. MR 26-743.Ul Polon. Math. 12(1962),65-70. l3l. Bielecki,A.; Krzyz, J.; Lewandowski,Z. On typicolly-realfunctions with a preassignedsecondcoefficient Bull. Acad. Poion. Sci. Ser. Sci. Math. Astronom. Phvs. l9(1962),205-208.MR 25-427' ll3, l5l 132. Biernacki,M. Sur quelquesmaiorontesde la th1oriedesfonctions univalentes.C. R. Acad. Sci. Paris 201(1935),256-258' Zbl 1 2 - 1 7 1 .u , 6 , l 0 l 133. Biernacki, M. Sur la reprdsentotionconforme des domaines lin\airement accessibles.Prace Mat. -Fix. 44(1936),793-314. Zbl t4-24. 129,49i 134. Biernacki,M. Sur lesfonctionsunivalentes.Mathematical2(1936)' 49-64.FM 62-375.[1, 6, 10] 135. Diernacri, M. Sur les fonctions multivalentesd'ordre p. C. R. Acad. Sci. Paris203(1936),449-451.Zbl 14-319'[3, 14, 17' 50] 136. Biernacki. M. Les Fonctions Multivalentes. Hermann et cie., Editors, 1938.Zbl 22-153. il4l conformedesdomuines?toilds. i37. Biernacki,M. Surla reprbsentotion Mathcmatica,Cluj. 16(1940),44-49-MR 2-84. [6, 18, l9] 138. Biernacki,M. Sur lesfonctions univalenteset k-symetriques.Bull. S c i .M a t h . ( 2 ) 6 9 ( 1 9 4 5 ) , 2 M - 2 1 4M. R 8 - 1 4 5 .[ 1 6 , 1 7 , 3 3 , 4 9 ] 139. Biernacki,id. Sur le moyenncsde module desfonctions holomorSect.A. 1, l-8(1946)' phes.Ann. Univ. MariaeCurie-sklodowska. 19,271 3, MR 9-576. (French.Folish surqmary). [], 140. Biernacki, M. Sur lesdomainescouvertspar desfonctions multi' 45-51.MR 8-326'[1, 14, 19] Bull. Sci.Math. (2)70(1946), valentes. l4l. Biernacki, M. Sur lesfonctions en m()yennemultivolenles.Bull. Sci.Math. (2)70(1946),5 I -76. MR 8-326. 19,14, 15, 19,2i, 33, 531 142. Biernacki, M. S)r une inelgatit| entre les rno!€nn€s des ddriv1es logarithmiques. Mathematica, Timisoara 23(1948), 54-59' I\4R 1 0 - 1 8 6[.6 , 1 0 , 1 5 ,6 3 , 6 4 , 6 8 ] 143. Biernacki, M. Surque[quesapplicotionsde kt formule de Parsevql. Sect.A. 4, (1950),23-40' Ann. Univ. Mariae Curie-Sklodowska. (French.Polishsummary)MR 13-123l47l

F FUNCTIONS (PART I) BIBLIOCF.APHY OF SCHLICHT

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p-wertigeFunktionen.DodatekRoczschwach 1ber M' Bicrnackt, 144. ' Mat' 22' 39(19;l)' (Polish)zbl45-187 ll4i nika Polsk.ro*L"' "irrirrtqaues Parseval' de de laformule app.ti)ations 145. Biernacki,M. Sect. A. 7(1953)' iI. Anrr. urirl vu.ia. curie-sklodowska. 5 - 1 4 ( 1 9 5 4 ) . (-P o l i s h ' R u s s i a n s u m tnarie')MR16-808'13'7'33'47''l coefficients de Taylor des 'fottctions les S" fU' Biernacki, 146. Sect' 9' ii. e".. Univ. Mariae curie-Sklodowska. univalentes. MR 19-540'[8' summaries) (1955),127-riJtiqsi'(Polish'Russian

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Mariaecurie-sttodowska.Sect.A.3(1954),71-79(1956).(Poiish' 17' 331 R u s s i a ns u m m a r y )M R 1 8 - 3 8 7 ' 1 3 ' lesextrem't Ccs modiiles des *oy'nn"'et les Sur M' Biernacki, 148. Sect'

klodowska' MariaeCurie-S f oncti ons oi'' r"'in"t' aii t 1'l"iv' (Polish' Russian summaries)MR 19(1956),127-136(1958)' A.

20-29".[3, 15] Tayloriens des fonctions 149. Biernacki, M' Sur les coefficienis C l . I V 4 ( 1 9 5 6 ) '5 - 8 ' M R Bull' Acad' P ; i ; t . S c i . univalentes. 1 7 - 9 5 7 .[ 8 ] coefficients cte Taylor des fonctions 150. tsiernacki, M. Sur les Sect' A Mariae Curie-skrodowska' univalentes'ri' enn' Univ' g(tqsz), r27-133.zbl 89-50' [8' l7] univalentes'Bull' Acad' des 151. Biernacki,M. s ur t,integrale foictions8(1960)'29-34' (Russian Phys' Poon. Sci Ser' Sci' Math' Astr' 16''24) summarY)MR 22A(1)-13?6'L4' l 5 2 . B i e r n a c k i , M ' K r z y z ' J ' O n t h e m o n o t o n i t yUniv' o f c e r tMariae a i n f u n Curiectionals Ann' anatytic of functions' theory the in (1957)' (Polish' Russian q(f qSS)' 134-147 Sklodowska'Sect' e' 16' 181 summaries)MR 19-736'13'7 ' l53.Bilimovitch,A.Surlamesurededeftexiond'unefonctionnon analytiquepgrrapporta'unefonction"analytique.C.R.Acad.Sci. 5 'R 1 5 - 5 2 1 '[ 5 9 ] P a r i s2 3 ? ( 1 g 5 3 \ , 6 9 4 - 6 9M desfonctions ncn analyti154. Bilimovitch, x.' sW lestransformations 1954-1956'MR 23A-50' ques. C. n' Acad' Sci' Paris 247(1958)'

zur TheorieschrichtenFunktionen. rss. Hirrruaurn,z. w. Beitr.dge FM 55-210'[9' 15' 27' 58] studiatvtathl't(tgz9),159"-190' Funktionen.Arch. Towarz'Nauk z.i . uai, schlichte 156.Brrnbantm, 'Zbl]-343' [6' l5' 68] p"vr' 5(1931)'233-237 Lwow.WvOz'-ftnui' 1 5 ? .B l a ke l ey,G.R.C/cssesofp- valen.tstar likefunction s .Pr oc .Am er . 14' 15' 63' 651 UA-253' 16' MR 152-157' 62)' 13(i9 Math. Soc'

t2

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1 5 9 . Bloch, A. Lesfonctions holomorphes et mdromorphes dans le cercle-unite.Paris, Gauthier-Villars(1926),FM 52-324' l59l 1 6 0.Blumenthal. L. M. Some relationshipsinvolving subordination. ' R 2l-830' [59] , 0 2 - 5 1 0M P r o c .A m e r . M a t h . S o c . l 0 ( 1 9 5 9 ) 5 1 6 1 . Boas, R. P. Univalentderivativesof entirefunctions. Duke Math. J. 6(1940),719-721.MR 2-82. U6' 281 1 6 2 . Bochner. S. tiber orthogonole SystemeanalytischerFunktionen. Math. Z. l4(r922), 180-207.FM 48-376' l59l 1 6 3 , Bohr, U. jber streckentreueund konforme Abbildung. Math. Z' l(1918), 403-420.FM 46-55E.[59] t g . Bohr, U. iber einenStotz von Edmund ! andqu. Scr. Bibl. Univ. H i e r o s o l y ml ( 1 9 2 3 ) ,N o . 2 , F M 4 9 - 7 l l ' [ 5 9 ] 1 6 5 . Bonnesen,T.; Fenchel,W. Theorieder konvexenKorper' Berlin' 1934.FM 60-673.[59] r 6 6 .Breusch,R. on the distribution of the valueso"f lf (z)l in the unit circle.Bull. Amer. Math. soc. 54(1948),l109-1114.MR 10-363.

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t 6 7 . Brown. R. K. On the partial sums of a iypically-7sqtfunction. Masterof ScienceThesis(1950),Rutgersuniv. Library. [13] power 1 6 8 . Brown, R. K. Sorre mappingproperties I'the meqnsums of p. Ph.D. orcer seriesun(i a problem in typicalty-reolfunctions of Thesis(1952),RutgersUniv. [13] Canad. J. Math. 1l(1959)' 169. Brown, R. K. Typicalty-realfunctio,ns. 122-130.MR 2l-662. [13] 170. Browtr, R. K. A classof t;'pically-real meromorphic functions. USASRDLTech.Report212l(1960)'[13,15,17'23'29'51'661 17l. Brown, R. K. Univaienceof Besselfunctions.Proc. Amer. Math. Soc. li(1960), 278-28?.tliR 22A(l\-455' [4, 28, 3ll l72.Brown'R.K.Llnivalent'.solulionsofw,,*D,'|=0'Carrad.J. 8 -R 2 3 A - i 5 9 ' 1 4 , 1 6 ,2 8 , 3 i l M a t h . 1 4 ( 1 9 6 ? ) , 6 9 - 7M Run' y. 173. Cacridis-Theoiorakopulos, tlber die urttere Grenze der deren f'(0) dungschranken $er beschrankten Funktionen f(z), vorgegeben,sl.N{ath'Ann.ll3(1936),656_664.FM62-370.u1' 12,22i der 174. Cacridis-Theodorakopulos, P' }ber die Krumm;tng NiveaukurvenderbeschranktenFunktionen.Math.Ann. 275-28'r.FM 63-287' U I, 12,221 I 14(1937), de 175. iakaiov itctrataicff;, l'. Sur I'univatencedc certainesclasses

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

I3

fo n cti o n s.A n n .Univ.SofiaFac.Phys..M ath.33( 1937) ,243 _252. "zbl 17-270.[4, 32,431 defonctionsanalytiques L' Surune classe 176. eakalon(TchakalofD' Paris 242(1955),437-439.MR univatentes.a.--n. ecae. Sci. 1 7 - 7 2 41. 4 , 9 , 4 3 1 of certain regionsof univolence . takalov(Tchakaioff)'L' Maxirnal Mat-.z. 1i(i959), 4A8-412' 177 of onalyticfunctions. UJrrainl closses nnglishsummary;MR 23A-416'1321 (Russian. de cerSi'r lesdoinairtesd'univolence t78. iakaiou (fctatafoi0, l-'lzv' Nauk Bulgar'lIuC' fiines ,tor,,';f p-ic''icns analytiques' 23A-r77' 129'62i Mat. Inst.4(l;60);No' 2, 43-5s'NIR a{ cenoinclusses Domainsof univalence 119. iakalcv (Tchakafoffl' L' -Dokladv l(1960)'No' 2' of analytictuiitiion'' SovietMatir' z"gt-rgr.MR 24A-50'[4, 32' 43) l 8 0 . b a k a l o v ( r c n a t d o r D , L . S u r ' l e . sBudapest d o m o i n e s r l ' uSect' n i v aMath' lencedes F'otvcs potynomes 11t^'.Univ' "';;;:;;iq""t 494'14'32' 431 ll lsz-ior ' MR 24A3-4(1960,/6r l S l . C a l l a h a n , J r ' , F ' P ' A n e x t r e : n a l p rMR o b l e22A(l)-959', mlo-r41-U nomials'Proc' 13',321 10(1959),754-i55' Soc. Math. Amer. pour et suffisantes ntcessaires rSz. a;l"ga.."no, C. Srr'tesconditions un cercle' d'une fonction holomorphe dans !,utiivo.le,tce 6(1932)'15-79'Zbt 5-18' 14'431 Mathematica l s 3 . C a l u g l r e a n o , G . S u r l e s f o n c t i o n s u n i15-26' v a l e nMR t e s17-472' . | | . A c a[4' d.R'P. Fil' Cluj' Stud'Cerc'Sti' 5(1954)' Romane. par' on univolentfunctions and 1g4.3"ilLi, p. some observations Inst' Univ' Nac' Litoral' Publ' ticularcto"l]'ii'm' Fac'Ci' Mat' 16',17-'18',42',45', 52' 54]' 8), lg5-2.2}MR I I-ttt' 13',7', Mat. 8(194 der Koeffizienten r85. carath6"d;i;:'c. 0;;; ;;^ vuriabititatsbereich vonPotenzreihen,diegegebenewertenichtannehrlen.Math.Ann. FM 38- 448'[s9] 6 4 (1 9 0 7 ),9 5- l15' der Fourier'schen lg6. carath6odory,C. (Jberden viriabilitatsbereich Funktionen'Rend' Cir' ho'm'onischen Konstanrcnvon positiuen jzirqr D, lg3-217' FM 42-429'lzi Mat. Paler*o l 8 T . C a r a t h 6 o d o r y , C ' U b e r d i e B e g r e n z'73(lgl2'), u n g e i n f323-370' a c h z u s aFM men"n. Geibiete. ilh. *rnnongrni, 4 -7 s'|.l s9 l l83.Carath6odory,C.ElementarerBeweisfurdenFundanrcntalsatzder Springer, Berlin' don\ormei-'Abbildung. scrr*arz-restschrift, (tqi+), r9-4r. FM 4.s-667'[591 Math' i. iiu* a-rr'-itudyrrheRundungsschranke' rg9. carattr6ooo*.v,'

I

14

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

Ann. 79(1919),402. FM 47'327' ll01 Cambridge, 1932. rqO. Cu.uth6odory,'C. C'onformal Representqtion. z b l 5 - 1 6 8 .[ 5 9 ] lemma. Bull. l9l. Carath6odoiy, C. A generalizationof Schwarz's -241' Zbl 16-216'[l 5' 22' 37| Amer. Math. Soc' a3(19 37), 231 2nd Ed. cambridge tgz.'cararh6odory, C. Conformal Representation. TractsintUatfr.-Phys',No'28'Cambridge'attheUniversity Press,1952.ll5 PP' MR 13-734'[591 ChelseaPubl' Co" 193. a;-rarh6odory,C-.-Theoryof Functions. I, tI' N e w Y o r k , l g 5 4 -M R l 5 - 6 1 2' U 9 , 2 2 ' 3 1 ' 4 6 1 , dons Ie cercle bornte d'unefonction cocfficients les Sur F. Carlson, 194. ^' pp, (1940).MR 2-165. ,iii;. Ark. Mat. Astr. Fys. 2TA, No. 1, 8 ll7 ,22, 301 lg5.Cartwright,M.L.onanalyticfunctionsregularintheunitcircle'|. Quart.J.Math.,OxfordSer.4(1933),246_257.FM59_325.[59] lg6.Cartwriglrt,M.L.onanolyticfunctionsregularintheunitcircle. II.Quart.J.Math.,oxfordSer.6(1935),94-105,2b||1_358.[2'3] lgT.Cartwright,M.L.Someinequalitiesinthetheoryoffunctions. ' M 6l-351'[14'l5' 65] M a t h . A n n . ! 1 l ( 1 9 3 5 )9, 8 - 1 1 8 F Z.-Su" Iesfonciions extrentolesdans lesfamilles de 198. d;;;f"ut, Colloq' Math' l(1948)' 168-170'122'241 for:ctionsunivalentes. bornees.Rozprawy 199. Charzyfiski,Z. Sur lesfonctions univalentes l l l a t " 2 ( 1 9 5 3 )5, 8 P P .M R l 5 - 2 3 ' [ 2 4 ] ii, t^ fonctioni uiivalentes algebriquesborn6es' 200. g;;;ri;rUi,'2. 4l pp' MR 11-25' 1281 RozprawyMat. 10(1955), la theorie des fonc201. ah;;rvfirt i, Z. Methodes variationelles clans Phys' R' P' Routionsunivalentes.Bull' Math' Soc' Sci' Math' 281 ' maine. (N. S ) l(49) Og5'7),259'2&' MR 20-544 122' Polynomes inverses' ZOZ. Citrz.yiski, Z. Fonctions univalentes univalentes.Soc.Sci.LettresLodz.Bull.Cl.IIIg(1958)'No.7,21 . 124,121 pp. MR 22A(1)-807 'Ciu.zyirski, Z.; laniwski, W. Sur l'1quation g;nerale des.fonczOl. bornees' tionsixtrbmales dans lo famille desfonctions univclentes Ann.Unir,.MariaeCurie-SklodowskaSect.A4(1950)'41-56' (French.Polish summary)MR l3-122' l22l de variailon des coeffZO+. Efrarzyfiski, Z.; Janowrti. W. Do:naine cientsA2et43desfonctionsunivalentesetbornees.Bull.Soc.Sci.

No. 4, 29 pp'MR 23A-732'122'24'291 LettresL6t .-rq(r9sq),

conZ.; Schiffet, M' A new proof of the Bieberbach 205. C;;rf"ti, jecture for' thi fourth coeffic.ient.Arch. Rational Mecir. Anal. 2'l 42' 53' 511 i(tqoo), 187-19j. MR 22A(l)-965' l-4' 17' 24' ' Z.; Schiffer,M' A geometricl'roof of the Bieberbach 206. C;;;ttnJi,

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHI ICHT

15

conjecturefor:!;cfourthcoefficient.ScriptaMath.25(1960)' ' U 7 ' 2 4 ' ,5 4 1 1 7 3 - 1 8.1M R 2 2 A ( l ) - 1 6 2 9 Acad' of schlichtfinctions'-f-tot' Imp' 20?. Chen, K. On 'i')i'o'v ' Zbl8-168' Il7 ' 42' 45' 5'l Jap. 9(1933),465-46'7 Math J' schtlicht functions' Tohoku 208. Chen, K. On iie theor:'of 3 9 ' 4, 5 ' , ^ 5 2 ] ' M 6 1 - 1 1 5 3[' 1 4 ' 1 7' , 4 0 ( 1 9 3 5 )1,6 0 - I 7 4 F Tohoku to ihe rheiry of schticht-fu-nctictns' 209. Chen,K. Cr''ntribtutians qlil , 125-"47.Zbl 12-214'[9' 15' 58] N,Iath.l. +f tf 2 l 0 C h t r r c h i l l , R ' V ' l n t r o d u c t i o n i o C o m pMR l e xItJ-439' V a r i o b lt59l esortdApplica' 1948' tions.NewYork, t''ttC'"*-Hill' coefficiei;tsin the expanSin on the argumentsof the ztt. {i^i;;;;' MR Ac-"aI\iath. Sinica4(1954),81-86' sion of a univalerrtfunction. 1 7 - 1 4 2 .[ 4 ' 3 9 ] et cerles z'ros desfonction's mbromorphes S" ni' C\orhnescu' 212. gult' Math' Soc' Romaine Sci' nines classesde polyn6t"'' Ill 3?(1936),9-11. zbl Oxof integraifunctions' J' Math" "4-220' (Jnitalent regicns 213. Clunie, J' NlR 16-809't28l ford Ser(2)5(19s4),2sl-296' J' London merom.orphicin the-u'nitclrcle' 214. Clunie, J ' On functions NIR 18-884'[59] Math. Soc' lZ(tq 57)' 65-67' 215.Clunie,J'OnschLlichrfunctions'Ann'lr{aih'(2)69(1959)' 25ll 511-519.iliR 2l-1194' 19' l7 ' Math' sciticnt functions. J. London 216. cruni e, I, on meromorpnic

z'ls-216'MR 2l-1064'16'9' i7 ' 25i sg')i, Soc.34(19

2 1 7 . C l u n i e , J . ; K e o g h , F ' R ' O n s t a r l i k e a nMR d c o22A(l)-295'14', n v e x s c h t i c h6', tfunctions' 2Zg-233' 35(1960)i' Soc' Math' London J. 1 0 ,1 7 ,1 8 , 3 6 , 3 8 1 C' R' Acad' Lundou-Carath?odory' 218. Comb.r,l' J" l" th\oiemede 41-42'MR 9-363' U9l Sci.Paris 228(1949)' o7onolyticfunctions'DukeMath' 219. Conn.ff, e' N' On th' p'op"ti" M1R' 2 3 4 - 5 0 [' 5 9 ] J.28(1961),73-8 in, Theoryaf Functionsof o' 220. Copson,E. i..qn Introductitonio Zbl12-169'[59] Complexio'ioOt'' Oxford' lg35' 2 2 l . C o t l a r , M . - F " ' t i o n s w h i c h a r e u n i v a Mat' l e i l oUniv' n a s uNac' b s e tLitoral ofthebounInst' regularily'-Publ' of domain a of dary 621 ' 4(1912),oi-gg. (spanistrlMR 4-155 149' bei air 'qOAiUungsfunktionen 222. Couranr,R. 7ber eine nigrn-rc:'noi 45-668' FM (1914)'101-109' konformerAbbildung'Gott' Nutit' und in der variationsrechnung 223. 8:lr.ant, R. (JberdirekteMethoden 7ll-736' FM e"". 97(1921',), uber verwandteFragen. viurn. s3 -4 8 8[5 . 9]

16

B I B L I O G R A P H YO F S C H L I C H T F U N C T I O N S

224.Corttant,R.Plateau'sproblemandDirechlet'sprinciple'Ann' Math. 38(1937),679-724'Zbl l'7-268' l59i Conformal-^Mapping snd 225. Courant, R."Dirichlet's Principle' N'Y'' 1950' 330 pp' MR Minimal Surfaces'IntersciencePub'' l2-90. [59] havinga positive real part in 226. Cowling,V' F. On analyticfunctions MR l7_1070. 329_330. theunit circle,Amer.Math. Mon. 63(1956), 1 2 ,1 7, 2 l l c. some apprications of the 227. cowling, v. F.; Royster, w. Math. Soc. Japan l3(1961)' weierstrassmeon vati"etheorem. J. 104-108.MR 23A-732. l4l J' London Math' 228. Crum, M. M.; p'op"iy of schlichtfunctions' ' R l8-121' [34] S o c .3 l ( 1 9 5 6 ) ,4 9 3 - 4 9 4M analytic in o circle' A:ta 229. Cyu, F. Som'eproperties of functions Math.sinica-q(1q59),382-388.(Chinese.Russiansummary)MR 23A-33s. l41l 2 3 0 . D a i o v i t c h , V . S u r l , e x i s t e n c e d e v a l e u r s l i m i t e s dMath' e l a r ePhys' sultanrcdes Ha''6 ) l ' Bull' Soc' ls classe a appartenant fonctions 471 Serbie8(1956),23-28'MR 20-874' 13' univolentfunctions on Qnan231. Danilevskii,e. rur. on single-volued -Zap' Mat' Otd' Fiz' -itr'at' nulus.Har'kov Gos' Univ' lJc' Zap' 34 R u s s i a nM ) R F a k i H a r , k o vM a t . o b s c . ( 4 ) 2 2 ( | . g 5 u , 5 1 - 5 3 ( 1 9 5 1 ) . 1 7 - 1 0 6 9[ .1 , l 5 ' 1 8 , 4 8 ] 232.Darwin,C''()n'sometransformationsinvolvingellipticfunctions, 1 l - 3 4 1 '[ 5 9 ] P h i l . M a g a z i n (e7 ) 4 l ( 1 9 5 0 ) i' - i l ' M R 233'Davis,P.J.Packinginequalitiesforcircles.Mich.Math.J. 10(1963),25-3r. MR 26-981' [2] poriur., H. On tie'zgros of total setsof polynomiols' 234. Davis, p. r.; Trans.Amer.Math.Soc.T2(1952),82-|03.MR13-552.[9,15,19, 49, 53,681 2 3 5 . d e B r u i j : , N . G . S i n S a t z i l b e r s c h l i c h t e F u n k t i o n eI n .Nederl..Akad 9' 7' 25'16'38' [ 6 ' 4 ( 1 9 1 1 ) ' 4 ' l 4 9 ' M F . 2 2 7 4 ' P r o c ' Wetensch., 411 conforme' C' R' Acad' Sci' Paris 236. Denjoy, A. Sar ltr reprdsentation 2 l g ( r 9 4 4 ) , 1 1 - 1 4M . R ?-287'[lE' 62] confcrne des aires planes' 237. Denioy, e.- sar la repr\seniutirrn ]VlaLhematicaTin.20(|9M),73_89.MF-6_262.[18'62] 238.Detwif.r,g.;Royster,W'C'Avariationalfor.mulaforluncticns convexinthedirectionoftheimaginaryaxts.Abstract568_2, 242' 124' 4ll, NoticesAmer. Math' Soc' 7(1960)' Press,oxftrrd, l93l ' zbl 23g. Dienes, p . The Taylor Seriesciaiendon 3 - 1 5 5 '[ 4 4 ]

FUNCTIONS BIBLIOCRAPHY OF SCHLICHT

(PART I)

I"I

polynomes' C' lt' Sur le rayon d'univalence des 140. Dieudonn6' J' 7 9 - 8 1 'Z b i r - 1 8 ' 1 3 2 ' 4 3 1 A c a d .s . i . p u r i , r 9 2 ( 1 9 3 i ) ' 2 4 l . D i e u d o n n 6 , J . . S l l t l e s f c n c t i o n s u n6' i v i7 ale t e s45', . C52', . R .547 Acad.Sci.Paris 39', ' n lgz(1g31),I148-1150'zbl 1-344'[4' relatifs cux dur quelqucsprc-u;-le''nes 242. Dieudonn6,J' Recherches d'une variablecomplexe' Ann' polynomeset auxfonctions borneis 14'ls' 17'

[6' 11' Norm.iii'istigir),247-3s8'zbr3-rl9' Ecole

6.ll 22,32,39, 42,43,45' 52,54' et de convexitbde cerd'itoilement rayons 243. Dieudonn6,i' S''' les tainesfonctions.C.R.Acad.Sci.Parisl96(1933),3.7_39.2b|6_64' [6, 10, 11, 12, 28] j' Lo Theorie Analyiique CesPolynomesd'une 24+. D'euJcnn6, M' 1938' [59] Voriable.Gauthier-Villars'Paris''a of funcof proof formuto i1 t'n-e lneorv 245. Dinghur, A' 7 ' impte 101-102'MR l6-231' [59] tions.Math. Student' iz!gsq\' 246.Dinghas,A.VerzerrungsschrankenbeischlichtenAbbildhngeildes 413-416'MR 21-517' I'14' Einhcit:krei'es' nrct'' Math' 8(1957)' 1 5 , 4 2 , 6 5 ,6 8 ] Theorie der p,l'huu einige Monotoniesiitze in der 247. Dinghas, Norske vid. Akad. oslo I(1959)' schlicrttenFlunktionen.Avhdl. 10' i5' 35'42'64'68f No. l, rs pp. i:ri.as-zg:' [6' problem in the theory of analytic.func24g. Doob, J. L.'iiinr^um MR 3-76' [59] 413-.424' tions.Duke Math' J' 8(1941)' problert of Plateau' Trans' Amer' 249. Douglas, J . Solutionof the ' bl3-328' [59] M a t h ' S o c .3 3 ( 1 9 3 \ , 2 6 3 - 3 2 1 Z valeurs d'ttne sph,rique d^crite!::^l:t 250. Dufrernor, i''i'r'i'oi'i 214-219'MR Duli' Sci' Math' Q)' 65(1941)' fonction *6'oio'pfte'

2s1.f:f6*llri;itl

d'un th,orime sur unenouvered,monstration

[46] d'Ahlfors'C' n' Acad'Sci'Paris212(lg4l)'662-665'MR3-81' m6ro' des fonctions 252. Dufresnoy,J. Sur lescercles'ie-ie'mpt*iage mo rp h e s.i .n.l.uo.Sci.Par is2|4( |942) ,461_469.MR4- 138.[46] -(2) 2 5 3 .D u fre sn o y' J.Sur lesfonctionsm\r omzt-re or phesetunivgle . MR 7-56. [62]ntes dans l e 6g(r94i.1, Math. Sci. Bull. cercreunite. fonc' pour certaines 254. Dufrernor,';.";; pronD*, iei coefficients Ser. Fenn. Sci. Ann. Acad. tionsmiromorphesdansle,,,il, unit-6' A. L, No. 25079(1958),7 pp' MR 20-968'1221of onalyticfuncproperties -i'n L. E. Certainextremal 255. Dundudenko, a circutai ring. ukrain. MaL z' tionsgiven in a circte and ft4n fq-ZS'[6' 10' 14' 15' 17'22'30' 8(1956),l'll-Zgti (Russian) 9 5, 0 , 6 1 ,6 3 ' 6 4 ' 6 5 1 3 5 ,3 6 ,3 8 , 4 8 , 4-i.Funktionen,welcheim Kreis 256. Dundut.ntll r-l inrr'rinis, itoti.-

-7

lE

BIBLIOGRAPHY

OF SCHLICHT

FUNCTIONS

S') 3(1957)' inst' Politehn'l'utr'lN' 2a-'7'll' 14' sind'Bul schlicht MR \z\ < 1/'f2 nou*liliu" tt"t**tes) cerman' (nu"'un' 3?-38'

,,"i;';:i,'r-ii"?;,i,i.lfl :'il:';:{;:!:#^;xi1!![i'K::";i:':' s y m m e t r yt z' v ' 1 { " " ^i r i

41I

r s a I 1 5 .1 7, 2 3 ' ilr-:;l:il1 runctions ,,o,r,ke , rnu,,i"uni ;))t,,ir";il1\t), 84_e5. -Fiz' (3) E' Deformatton

uunu;:'ij il:lluil'"Ser' Mat' io'i+' 258 lau::ril,ln::x;'il-";l1ijlo+o

L' zse' ;"ndud'enko'

i!, zl, 53,651

f#:; -..^--rization of ctassef : ffi;'1'::

Dunut: ;,!ti* zsg :::; 35*41'i(Russtan' *h', ","*'' " )MR ** t' $i::;;* lnst' S(1q61)'

031.. ,'^ iip,-ty. [4, 15,17r Kas'janjuk'S" !: ''o'n'';{;uy'i u t{:::'6i; i Dunduttnio"i Mat' NaukI){ 200. )i'on"o'nulry ^Y:tohi' univalent [6' l5' 49'o!l,nrlr,,, funct'to'ts 23A^-475' *R 'o tiitrt'""1 "f' r65-170.

?' ::T.:::{;'l?'";1tf;;*'i'ii;i"t'n;5 . Dund"t'"x"' 26r to sPecialclosses' ^' belonging

(re56),"J:t;f*nli-loosl[1ti''io-r5'r7'22'30'35'35'38' +s'so'l"ii]'rlt . onuniuatent o:'?:."[r!]{',,'i:;:ir:;, func.tio: *.sDund'u':f'o*ioYo"n"j.'*urr. 262' '"" Jt'uin .'i.'r*'*t H;. iii,-is,zl

:l,'"l lJ'iJ t"?g,";, ii'"'$i'" i Dund"e*u"'

1;;;ii inIn" i"^r'

^qn::J' 1,i-?Li'Ti":J'ffi1;'f1#fi:"ilI Dopovid' MR 20-vou' (Jz)-'. .ili;"rrilil^'ru**aries) < sumrn \z\ Russian'English

263

(-lxrainian' 5g5-5g'7'

tj:'t.'l,' estintatest o'yli*''t!'{i{i'"ii e o c j ff L : ; 1i,12t. ,r^ ;ri;Tj ananor ,I;i iJ.li1ttiuI',l,u,l;,)t?;#"",]i,ffi)iit1 .Amer

;l y,,; ; s iu,,n,I z6 I ii i'1,i,ii, ;k,?IJ;, ;Ji'i,r: i;;f-;;ar. i: :2:, s(rsoz), irr.,, "T:::::;, .i;;. 266.Dure",";:,i.;-i.t T,f . in an annultts"

schlicht [48] .rL260-2'l'2.MR 25-39thpnrv of the secondt'ariafion,in^*

u,r,eMath o,, l, :;;.' i .' l! { 1i i,.y ; f,,,n z6.tDure":r .;r i.t irfo'!n!' l,/,,i f "T ' lz4' temum Problems 42't'L 63(1e33)' y* ?,1-uo va ,. Mat.Fvs. ,otrnJli"nr:;;?" lesfonctioiisunivalentes'

268' Dvor;i"'6:-sur

q tz,y, o?)r zvls_t e_r6. " r,o,,o i:J"!!J,"{)i.^iii,,,t;,,;_i Aryeh.t,'

26e.Dvorerzky,

l:;;;,'Zoi_Jol.nnq

221' lt> Acad' Sci' Paris

I) FUI']CTIONS(PART BIBLIOCRAPHY OF SCHLICHT

19

2 T 0 . D v o r e t z k y , A r y e h . L e s c o e f fs"i:";;ir i c i e n t s d , uizslgn), n e f o n c t i o447-44e' n u n i v a l eMR nteetle

;;#. r,oi."c'."R." domaine

21r.9:;;"[?],

funcunivatent -of Arych, Boundsfor the coefficients u7' r2-r2'7' MR

sL.' I ii;;0i;;2e-63s' r'1",t,. Bull'Soc'Sci'Lettres Lowner' Equation-s'n"!tlde r' ,rr.1;;rlrll'ru', 12'22'241 MR23A-732' derraLtdi. rLtrqo0llil;'+ a 09, vr.. dasKoeffizientproblern w ;r;;fi.rr, 273.Effertz,F.;1; ii''po'iti"* ieattetl'trsh' N{ath'i2(I961)' ;;;. ticns.proc.

ilonalenn'n'i'':i"

ttie n a" - 1:!2!etischen Mizbr e h art c s n J',Zt,, o 7 u );'f, r#li] 22r-230' , - i:;X? irinri. ffi1--t. 42(rs3'7), dergeome,i,rirri"^' ,r. f#"f;,!:'tlt"l)

de detasurface topotogiques y'ryy:.':'.oprietts zbl 12-228't34l

767-272' sphire.rt"a' r"rtit'' zs(tq:s)' thefuncli3n'W: Az + B' ';; Levine' S'; E' ";MR 21-1190' 216.Elvash, *j' [59] 303' o6(rqsg)' Amer.rt'ru,il''ruron' 2 l T . I 1 p s t e i , , , g . s o . e i n e q u a l i t i e s r e l a tfuutn' i n g t o cStc' o n f o53(1947)' r m o l m a813-819' ppmgupon euil' '\;l;' slir-domain''' canonical 601 . 19,l7 ' 18'25' 2'7-', schlicht MR 9-180 ' Oi o coniectureconcerning 278. Epstein,B'; Schoenberg'I'.]

functions'';;ii''A'ttti'M";:"s;;'"6s(1e5e)'2't3-2't5'MR

whose 'J;11].; Taylorseries G. Schltcht Piranian, ' l'f;J,i;J]| ,,.

convergenceontieunitcircle.is,uniformbutnotabsolute.Pacific

t62l MR 13-335' J. Math.itrisil, 7s-82' gewisserFunktionen280. Erwe, ' ' i)ii'' aii' s;'t'tr't'theitsschranken ' 3el te' 2'7 MR 14-269' so(rgszl''il-e+ i' of thederiva.tive famitien'i;' rilation irr*rrr'rne moclulus

2g1. Erysou,s.'p.-o-othe 63] andthemodulusofthefun-ctioifo,univalentconformalmgpplngs. U"f" 1954'(Russian)[15' Sarlt"" dissertation' of Summary iunctions' D'povidi i ,y;;;; Russtan' 282. irzohi, r. G. on sonte "i "a::t 'iseo-)soq"(ukrainian' ns* trila ukrain' Nauk Akad' [5' 6' 14' 15' 63'64'65] Il' Mat' English with^integer'1o;fficienls' "il**itt)' Pou'er^s-11iis A' M' Evgrafov, 283. MR l3- 335'[3 91 izr - 132'( Russian) S b o rn i k'N ' S' 29( 7- .) tr qsr ) ' 284.Evgrafov,M'A'Pow'e,rs"n'*i'nintegralcoefficients'l'Mat'Sb'

i!:: Ns,6i ii*'l:l:lli:lT;lyml,ni,l;{:,i,;}"}, r:, Munchen ekai'wiss

"' f,,,7;,f;X{f,i'rffi'-{il;;;;'"e""' 46-550' [9',18] (1916)'39-42'FM

-

2O

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

(1920)' 2 8 6 . F a b e r , G , I J b e r P o t e n t i a l t h e o ra'ftuO' i e u n d kWiss' o n f o rMunchen meAbbild ung.Sitnuyt'' -phys' Kl zgsber. tvtath'

Ab' konformen de.r aufderrheorie Munchen

,r, ?^;7,,y,ir;'htl|)y0,,,1,pt'vt''fi' Math' bildung'sitzgsber'

Bayer'Akad' Wiss'

[5e] gr-1oo' FM 48-1231' l of Trgaz>i M' R. O:nopp'o*imqp1'Ut functions

288. Farrell,O' J'; Bolster' Proc' Amer' M;;: lesservolencei''

S"t' 13(1962)'158-162'MR

Dokl' derivative'f a ctmptexfunction' the on s. ,rn.';;::"il-}. MR 10-288'[4] Akad. NuY.ksisn tN s'l e:trq+8)'"35?-3s8j 2 g 0 . Fe j 6 r,L .tJb e rd i e K o i tver genzder .Potenzr eiheander Konver gen. zgrenzei,,;"i;;iert
portiatsummen und ihreMi ueIwerte ie d e.r b i) s e h i c o,,, n ,nu.,!":!1,'1.2, b e i d e r F o u r i e r r e i h e u t t d r i t i n z r20' e;ne.Z.Angew.Math.Niech. ;0-88' FM 59-298'[4',-10', ?,9 : .2, I 3(1933), monoiibir'Pctenzreihenmit mehrfoch vol' 8 y. un urn rrn Jnirl, ej€r, F ?g1. ac Scientiarum' At;; ;il'utt"n rcner Koeffizien4snfolge' 39i (1936),aq-irs' zbl 16-108'[4' 6', monoton'egyutthotosoiozat' tobbszorosen 298. Fej6r,y' noi'oni'o'ok E'ttttito' 55(1936)'l-29' /a/. Matematikait' ft'*t"Jtii'aoln-yi mehrfaclt Reihenunripotenzreihenmi; 2g9. F;r6' ,L. Trigonometrische monorcnerKoeffizient'nfots'"'i'unt-e^tr'Math'Soc'39(1936)'

'?],

funktionentheoretische Riesz' L .tibe' einige ,*. itl??; -:lrq' [3' 7] FM 48-327' tds Math'z' riiiqzri' ungteichungen'

FUNCTIONS (PART D BIBLIOGRAPHY OF SCHLICqT

2I

3 " "0^1' . F e j 6 r , L . ; S z e g t i , G ' s p e c i a l c o n f o r m o l m a p p i n g s ' D u k e M a ' r i t ' J '

20.'41'491 i g i r q 5 l ) , 5 3 5 i 5 4 8[ 6' , l 0 ' 1 6 ' der Wirzein bei gewtssen Verteilung ait Ai"'M. Math' 302. Fekete, mit eoizzahttsenKoeffizienten' Gleichungen algebraischen -il FM 4e-47't59l nogzt),228.-24e' ebener den transfin'iten Durchmesser 303. Fekete, M' 0b" FM 56-112'[59] II' Math' Z' 320;3q'215-22L Punktmengen, schlichte ungerade O' Eine-Beme':k'ngiber 304. Fekete,M.; 3*", i"{atir.scc. s(tr:3), 85-89.Zbl6-353' Funktioxen;.;i;con

Dokl' p-uatent for some-e.stjyyles .functions' f15;dl;;1]';1'r 30s. MR l5-413'[3' 14' s') e2(1953i'zti-zqz' Akad Na'rkbJsROt

17' 49' 501 connectedwitit On certarn tzrtremal domains Meh' 306. Fel'dman, Y' S' t-eningtaa' Un-tY:Ser' Mat' univalent f)n':tion'' Vestnik 49' 681 2 ' - 6 7 - 8 5 't u f n Z S - f2 1 1 ' U 5 ' A s t r o n o m ' 1 8 ( 1 9 6 3 )N' o ' meromorphen i^ Einheitskreis ilb"ii' 307. F'enchel,w s c h l i c l i e n F ' m l : t i o n e n ' s i t z s b e r ' p ' * t t ' A k19] ad'Wiss'Phys'-Math' ";;;;;i"^g'n f, +: t-436'Zbr2-269'[9' Kl. H ZZtzttigt su de la repr^sentationconl-orme Etude (Lelong) J. 30g. Ferran.J. (3) 59(|942), s.i. 6.oi. Norm. Sup. voisinagede la frontie.re.Ann. 43-106. MR 6-207' 146'62) C' R' Acad' Sur un-th\orime de M' Golusin' 309. Ferrand,J' (Lelong)

MR 5-e4'uel Sci.Pariszii(tg+ii,2s4-2ss' holomorphesdans une

l,esfonctions 310. Ferrand, J' (Lelong)Sur MR 6-262'[19] (Z)'ellgqi)t +'Z'4I1' Math' Sci' couronne'Bull' son apptication i'nliu'ititaa;e1t13rs^et 31I . Ferra"d,J:G;t""tl'i';;' ouprobli^ii,ti,d6riv6ea),eutaire.Bull.Soc.Math.France '72(is4/i),r'78-192'MR ?-ss' [46] domcir"' aitoi*otry^o'n1l:!que d'urt 312. Ferrand,J. Gelong)Sur la c.R.A.";'';;i:'i*izzt
BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

harmonic 317. Flett, T. M. Some remarks on schlicht functions ond J. Math. oxford func'tions of uniformly bounded variution. Quart. Ser. (2) 6(1955),59-72.MR l6-916' 123,621 J ' Math' 318. Flett, T. M. O,nthe rqdial order of a univalentfunction. Soc. Japan l1(1959),l-3. MR 20-662' 162l 319. Fcrd, L. R. Automorphic Functions. New York, McGraw-Hill, (1929).FM 55-810. [59] 320. Ford, L. R. On properties of regions which persist in subregions J. bounded by levet curves of the Green'sfunction Duke Math. 1(1935),103-104.Zbl rl-261. [], 37, 60i en321. FourBs,L. Sur lesdomoinesd'univalencede certainesfonctions MR 9-507.[28] ti)res.C. R. Acad. Sci.Paris226-1948),1157-1159. une fonction admettant 322. Four|s, L. Fonctions analytiques d'outomorphie donnee. c. R. Acad. Sci. Paris 232{1951),, MR l3-222. l49l 1894-1895. Power serieseXpanSions Jor inversefunctions. Amer' S. 323. Frame, J. Math Monthly 64(1957),236-240'MR 19-22' [59] verzer324. Frank, P.; Liiwner, K. Eine Anwendung desKoebeschen rungssatzesaufeinProblemderHydrodynamik.Math.Z.3(|9|9), 78-86.FM 47-326.[59] J' Lon325. Frazer,H. Further inequalitiesin the theory of functions. l 5 ' 6 5 ] d o n M a t h . S o c . 1 0 ( 1 9 3 5 )1,4 3 - 1 5 0F' M 6 1 - 3 5 1 '[ 1 4 ' London 326. Frazer, H. on funrctions regular in a convex region. J. Ir4ath.Soc. 20(1945),199-204.MR 8-19' [59] Acta 327. Freud, G. (Jber einen Reihentheoretischer'satz von Fpier. MathAcad.SciHungar3(|952),1^73_|76.(Russiansummary)MR 14-737.14,221 32S.Fridman,G.A.ontheproblemofthecoefficientsoffunctionsof the classF/a. Dokl. Akad. Nauk sssR (N. S.) 65(1949)'805-808. (Russian)MR 10-602. 13' 171 Duke 329. Fnedmati, Bernard Two thqorems on schiicht functions' M a t h . J . l 3 ( 1 9 4 6 ) ,1 7 l - 1 7 7 .M R 8 - 2 2' 1 1 7 , 3 9 ,5 + l von 330. Fritsch, w. uber konvexe und schlichte Abbildungen -122. -M5 .'Zbl 17 U4, en. DeutscheMath. 2(1937),121 K reisbereicft 2 2 , 3 2 ,4 3 1 331. Frostman,o. sur lesproduits de Blaschk;. Iiungl. Fysiografiska Soc. Sallskapetsi l-und l;orhandlingar (Proc. Roy. Phvsicg. Lundj) 12, No. 15,(1942), 169-182'MR 6-262' t59l and 332. Fuchs, B. A.; Levin, Y. l. Functions of a complex variable 1961, some of their applications.@nglishtrans.) PergamonPress, 286 pp. Zbl 98-276. l59i

t;rF

(PART I) SCHLICHT FUNCTIONS BIBLIOGRAPHY OF

23

t s,I:j ::.'l I':r:W #:1'$ilil# i:!::it: 333Fuch No' 1' Jan' Univ. August il'f,'J,i Amer. fnfuttt'Soc' 68' Bull' No. 6(1961)'pp'483-485;

of anaivtic for ;neartv1t-ttes theorem )|u')'r""'ss ' MR5-36' l.0 l?,ik:t-:tiT rto"n't*' iiios(rg+l)'35-47 i*J"t functions.p'ot' '

, cerivativeand convexfunctions' 13, e,10, buil'lt*; soz ro i+, rs i.,rn :::--:i1iiir,";;_;; 1":1, lsll

derivative and convex generqliz^ed'-schwarzion A ' F R' 336. Gabriel,

311

ftnctions'otttit'I;th't''ooi\ii""oll-oze'MRle-lMs'[4'6'

of 1 0 ,1 4 ,3 1 1 the integralsof moduli concerning results Some M' R' 337. Gabriel, regularTu,i,'t:on,alongcertai,n""cu.rv,is.J.LondonMath.Soc.

ofmoduti.cf ,J'13',lJ,ii:;:lXii;?!:rr')ernins theintegrats ,,, r e g u l u r f u n c t i o n s o l o n g c u r v e s o f c e54-331' i t a i n t y p[3' e s101 ':Proc'London

tn'1zi'FM Math.soc'(2)'28(1928)'in'''['ott *oayti of regular functions R' fr" ci)'n"ins "i vruttt' Soc' (2)' 39(1935)' 339.Gabriel, fff; along'onu''i curves'Prcl' 'A";;;'''io^ [3' 10'-16] tnzbl 11-358' 216-231' andsubharmonrc positive i^'tions n'?' 340.Gabritr, Math.Soc.2|(|946)' convex,";,;;;."i:i"ndon closed a on and side

i.?:::,: Xl"''lh ::Aff: ifi ,o'8"i.?; l::'^i:iT,\iln=,r',

aber nicht absolutkonvergtet . l'1,621 14-737 3 4 2 .Ga i e r,D .sch lichtePotenzr eihenonder Konver genzgr enz e'M ath. t62l 15-113'

iso-qss'MR z. 58(1e5i)-, zurkonformen Ko'matu lteration'u"iii'n'von ein 865-885. 343.Gaier,p]fiw' vt.ct'. 6(1957), !|,i"r".t'. Ringg,oi,,,n|' Abbildungvon MR 20-18' [59] ,,- Durchftihrung t'..,.nhfiihntns der a konformen Abzur 344.Gaier, v' inti"uchungen bildungmehrfoch"'o*^'i0"tr["il'c:ebiite'Arch'Rat'Mech' t5el Pacific Anal.,tibi6i'iog-trs'MR21-728' /j'i::yto'regions' io'iv ^f i''* conformal on "i ,D' 345.Gaier

r r'r"ttr"zi ror runetjgl,s iZd|y!::r;;Yiii)':,' ,::"n],,^s

346.Gaier ,o,o,.iy:"::r:;:'

e(1e62)' o;.nl^*urionuiMech.Anal.

'ft'fn ZS-+O'F' 16' 48' 621 415-42L

-7

24

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

A note on the mean value of the 347. Galbraith, A. S.; Green, J' W' MR poissonkerntel.bull. Amer. Math. Soc. 53(1947),314-320. 8-51I . [59] Walsh' J' L' On the growth of 348. Galbraith, A. S'; Seidel,W'; Amer' Math' oifin'tfons omitting two value* Tlan;' derivatives 19',43',62] Soc. 67(194D:320-326' MR lr-344' [14' of univalent functions' Kiev349. Gal'perin, f.' Vf. On o class 189-l9l' MR 17-957'U0' Avtomobil-Doroztnst' Trudy 2(t9!5)' 1 7 , 2 3 , 2 8 ,3 8 1 univalentfunctions with boundeci 350. Gal,perin, t. iM. The theory o.f rotat!on.I,u.Vyss.I.rcebn.Zaved.Matematika(1958),No.3(4)' 7 18' 201 50-61. (Russian)NiR 24A-38' [2' 4' ' of the Toylor yriel of two speciol 351. Gal,perin,I. M.. Finite sectiotts clossesofunivalentfunctiorts.UspehiMat.Naukl3(1958)'No. ) R 2 l - 2 5 ) ' [ 2 0 '4 3 ] 5 ( 8 3 ) ,l 7 l - l ? 8 ' ( R u s s i a nM 352.Gal'perin,l.M.Ontheargf'(z)ofap-leavedstur-likefunction' Ukrain.Mat.Z.ll(1959),207-2|0.(Russian)MR22A(l)_128.[6' 24,491 of p-valent spiral -functions' 353. Gal'perin, I. M. On the theory DopovidiAkad.NaukUkrain.RSR(1959),1051-1053.fUkrairtian.Russian.Englishsummanes)MR22A(2)-1628'[6'14'15'23' 63,651 univalentfulctig.ns with bounded 354. Gal'perin, [. M' On the theor'yof RSR (l?60), i465-1468' rotation. Dopovidi Akad. Naui Ukrain. (Ukrainian.Russian.Englishsumrnaries)MR23A-330.|4,20,43] of functions of special c.lasses 355. Gal,perin, I. M. On tie theory rototional-symmetry'ukrain' schlichtin the unit circle with k-iupte M F . 2 6 - 2 7 7 '[ 1 0 ' 1 5 ' l 7 ' a t . 2 . 1 3 ( 1 9 ; l ) , N o . 4 , 8 8 - 9 2 '( R u s s i a n ) 23,38,64j of p-valent fu-nctions' Dopovidi 356. Gal'perin, I. M' On the theory Akad-NaukUkrain'RSR(1962)'i:SS-tSO0'-(jkrainian'Russian' l4' l5' 63' 64' 65] Inglish ru*mu'it') MR 26-7M' [i' 6' and the szegokernelfunction' p. 357. GaraU.aiun, i.'srh*orr's lemma MR ll-340' t59l Trans.Amer. Math' Soc' 67(1949)'1-35' of tength in co-nformalmapping' 358. Garabedian,P' R' Distortion 9 'R 1 1 - 2 1 '[ 5 9 ] D u k e M a t h . J . 1 6 ( 1 9 4 9 ) , 4 3 9 - 4 5M p' L' A remark on cavitationalflow' 359. Garabcdian, n'; Royden' H' Proc.Nat'Acad'Sci'U'S'A'39(1952)'57-6i'MR14-102'[59] L' The one-quortertheoremfor 360. Garabedian,P' R'; Royden' H' (2) 59(1954)'316-3z4' mean univa;lent.functions' Ann' of Math' . 6 , 1 9 ,2 4 , 3 3 1 M R 1 5 - 6 1 3U

-_

FUNCTIONS (PART T) BIBLiOGRAPHY OF SCHLICHT

25

the theory of R'; Schiffer' M' Identities in P' Garabedian, 361. Math' Soc' 65(1949)'187-238' conformal mapping' Trans' Amer'

t59l MR 10-522.

p. M' Convexityof ctomainfunctit'nals' 362. Carabedian, ir't Schiffer' 281-368'MR l5-62t' [591 J. d'AnalvseMattr'2(1952-53)' coniecp. M' A proof of theBieberbach 36'J.Garabedian, n't Schiffer' f u r e f o r t h e f o u r t h c o e f f i c i e n t . J . R a t i o45 nalMech.Anal.4(1955)' 27', 42', ', 52',53', 541 25 24' 17 ', 4' , -465. 1?-2 MR l;, 427 inequalityfor P' R': Schiffei' W' A coe'fficient 364. Garabedian, (2) 61(1955)'116-l16' MR schlicht lunctions'Ann' of Matb' - [9, 16, l'7, 24, 25, 39' 54] 16-579 of functionsunivaiellin theunit cir' 365. Garciu, p . oi'ti'''i'ift'r'ns MR 3-78'[i7' 76-8)' lSpanish) c/e.ActasAcad'Ci' iima 4(194i)' 45,52,541 W'K' An inequatityin thetheoryof con366. Gehring,F.W'; Hayman' pures Appl. (9) 4t(t962\,353361'MR uattr. mapprig..l. formar 26--1209. [7, 15, 24] 36?.Gel'fer,S'tC*fft'lZurTheorietlermultivalentenFunktionen' R e c . M a t h i M " . i | o r n i x ) N . S . 8 ( 5 0 ) ( 1 9 4 065] ),239_250.(Russian. l4' 15- ' 4:' Ge rma n,u ttu ty ) MR 2- 185'[1' de l''toilementet de luconvex36g. Gcl,f.r, s. tcu"rrirl su, Iesboines i t6 d e sfo n cti-ffi"lun' onsp- valentes.Rec.Math.(7-55' M at.Sbor nik) N.S.l 6( 58) MR [9' 1l ' 12' 14] Frenchsummary) 81-8;' (1945), Redc' propertyof A9u1ae!^{unctions' 369. Gel'fer,S' (Guelfer)On a (1945129-r-294'(Russian' Math. Ourui.iuornix) N' s' rotis) I 5' 2?' 37' 6l) E n g l i sh,u **u i v; MR 7- 288'[l l' whichdo not of regularfunc-tions 3?0. Gel,fer,s. (Guelf er)ort the crass (Mat' Sb') N' S' - '" Xtt' Math' takeon anypair of valuesw and 33-46.MR 8-573'U7' 341 19(1946), Dokl' it multiv-ulent.functions' 371. Gel,fer,S. (Guelfer)Thevuriot:iin qg pp' (jqs+)' sgs;'888'Amer' Math' Akad"Nauk SSSR(N' S') (z)ze,1ilo:1' 1-4' MR L6-459'l24l Soc.Trans,. 3 7 2 .Ge l ,fe r,S .(Guelfer ) oncoefficientsof.typicallyr ealfunc MR ti ons . (r9i4),3i3-3i6.(Russian) 94, s.l sssR cN. Nauk Akad. Dokr. 1 5 - 7 8 6[ .9 , 1 3, 1 7, 2 3 , 2 5 ,5 1 1 3 7 3 .Ge l 'fe r,S .(Guelfer ) Onthec' oefficientnr gA\y{ or pvalentfunc Amer' 955-958' 106q:s^6J' tions.Dokl.Akad' NauksssR iN' S') ' Il4'24' 421 17-957 Math. Soc.Transit'(2)26(1963)"5-10'MR of typicallyrealfunctions' 374. Gel,fer,s. (Guelfer)on the ,oiltritntt MR 2rr-2r3. (Russian) Dokl. Akad Nauk sssR (N. S;i l5(1957), 2 0 - 1 6 1[.1 3 ,1 7 ,4 5 , 5 1 , 5 2 1

-t

26

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

3 7 5 . Ge l 'fe r,S .(Gu e l fe r)Ontypicallyr ealfunctionsof^or der p' Amer ' MR 234- 330'U3' 15' 17' l536' (2 ) 1 8 (1961) ' T ra n sl ' S o c' Ma th . 3 9 ,5 1 , 6 6 1 3 7 6 . G e l ' f e r , S . ( G u e l f e r ) T h e m e t h o d o f v a r(2) i a t i o n s i n t h37-43' etheoryof yunitions.Arner.Marh.Soi. Transl. l8(1961), p-varent . 4 ,1 5 ,1 7 ,24, 50' 65] MR 2 3 A -3 3 0[1 varisof the Goluzin-schiffer 377. Gel,fer,s. (Guelfer)An extension Nauk Akad' regions'Dokl' tional methodto nrultiply-connectei MR 24A-612'124'601 (Russian) SSSR142(lgi2),503-5i)6' pour lesfonctions coc-fficients 3Tg. Geronimus,l.'iur le problemedes ' ' Zbl 16-125 R. e.ud' sci' uRsS N' s' l4(1937)'97-98 bornees.c. 13,221 3 ? 9 . Ge ro n i mu s,Y .L 'so meestim atesfor thecoeffic' ientsofbounded SSSRSer' Mat' 24(1960)'203-212' Nauk Akad' Izv' functions' 22' 30) iRussian;MR 22A-646'U7' positivereal!:rt,in a half-plane' 3g0. GoldU..g,t. i. Functiois with ' Zbl l0l-297' MR 29-264'l2l 133-33'9 Duke Math. J ' 29(1962), 38l.Goluzin,G.Onsomeestimatesforfunctions*!:hmapthecircle confor;nallynndunivalently'-nec'Ma^'h'Moscow36(1929)' FM 55-789'[6, 9, 10' 1l ' 15' 39',42]. 152-172. Re' der Funk.tionentheorie' 382. Goluzin,G- Zum Mojoraticniprinzip 14-69'lll Math. Moscou+z(tgis), &'7-649' zbl 3 8 3 . G o l u z i n . G . Z t t r T h e o r i e d e r s c h l i c h t e n k o n fl0' orm enAbbildungen. 15'39'49' 169-i90'Zbl12-409'[9' Mat. Sb.fN' S'l 42(1935)' 64, 581 384.Goluzin,G.Surlarepresentationconforme.N|at.Sb.(N.S.) 273-28r.Zbl 16-216't19l 43(1936), dansla theoriedesfonc385. Goiuzin,G. Sur leslllssremesdi 'ototion tionsunivalentes,Mat.Sb.43(1936),293-296.2b115_71.[6,15'581 336.Goluzin,G.ondistortiontheoremsofsch l i c h t c oGerman nformalmap(Russian' pings.nec. tviattt'Moscou(U' l(1936)'127-?5' iummarY)Zbl \4-221' U5' 681 3 8 T.Go i u zi n ,G.On d i sto r tion' n' l"uni' ' ' alentconfor malm opoingsof mu l ti p l yco n n e cte d dom ains' Mat' Sb' ( N' S' ) 2(58' 1937) 601 ' 37- 63' ( Rus 12' 15'29' sian.Germansummary)Zbll7-l2I' Ig' 388.Goluzin,c.Somehoundsforthecoefficientsofunivalentfi,nctions. Germansummary)Zbl Ivlat.Sb. N. S' 3(it33), 32i-33C'(Russian' 1 9 - 1 ? 1[ .1 4 ,1 5 ,1 7 ,5 0 , 6 5 ] of schlichtfunctions' of the coefficients 3g9. Goluzin,G. some estimates ivttg-ttt- U4' 15' 17'50' 651 Mat. Sb.Xrliai, 321-330'(Russian) der die verzeilwtgssiitze 3g0. Goluzin,G. Ergiinzungzur A.rbeig'"iit'er

FUNCTIONS (PART BIBLIOGRAPF]YOF SCHLICHT

I)

21

Moscou (2) Ahbildu-ngen"' Rec-'Ivlath' konformen schlicltten 58',681 rvr ol-zq2'lg'rs',24', 2(rg37),68s-66;' in a circte' theorennfor functions^regular co','e'ing Some G' 391. Golrvin, Mat.Sb.0\.S.)z(|g37),6|1-6';;:inu''io.'.Cerrna^iSulrllllar!)

',

Rec'Math' Futiktionen' s.chtichten l*'!"'n)he-orie.der German ,nr. [xg,f (Russian' 383-388' (NIat.suorniliN' i' iC-420939)' MR 1-308'[1' 15' 16-'24f i-nmma'Y) (Mat' Sbornik) '"iiite^punitioien Rec'Math' ii'"i G' Gcluzin, 393. Germansummarv)MR Gussian' 277-J!a' (1940)' 8(50) N. S. , 7, i9' 33' 531 Rec' 2 -1 8 5 Ig . , 1 4't)Oi' .1 der schlichtenFunktionen' ioeffizienten C' German 394. Gciuzir', rz6+) (1943)'40-47' (Russian' Math. (Mat' iu"*ttl ti' s' -i"5-91' [15' 17' 54' 68] ,rr**uiv) MR Rec' Math' der '''iti'n*n Funktionen' rniori'e 'i' G' sumGoluzin, German 395. 48-55'(Russian' (1943)'

(Mat.sirornirl)-x izt1il 58]

maty)MR 5-93' [9' l5' functions' of derivatetol!::d'd (Russian' 396. Goluzin, G' Someestimatesd iitsel (1945),295-306. Rec.Math. (Mat. Sbornik)| 6ll 22' 50' *r_1-202' itt' i+' 15' t7' English,"ti'irl Rec' Math' theo;vii^"':'it'nt {yy'ti:n's' L'nglish 397. Goluzin, c. oi'ttte (Russian' s 141097Qio-sl' tet-ttg' (Mat. suornit<-)"N' 58' 68] su mma rYMR ) ?- 515'[9' 15' ond sintilar protbre^;;iirreth'eodory-Fei'r the G,.'-on zin, Golu 39g. N' s' 18(60)(1946)'213-226' sbJintki Mat' rt'r"tt'' problems.ntt' S-22' [59] (Russian'U"tliti summary)MR for schlichtconform aistortion"tirori^i the on c.(1946)' 3gg. Golu,in, SUtrnik)N' S' 18(60)' representsi"' ntf' Math' On"' 379-3g0.(Russian'Englisht""t*"tJnu*g-sl+'ll5'29'45'67'681 of univatent th;;;;;'t and ccefficients 400. Golurin, i]oi"aitirti", s4'' 36' fu n cti o n s'i l' M;th' M atst"ttir lN' s' 1i( ( 1946) ' 183202 l5' 17'M' 8' e' [6'61) nip i:iis'

;;;]i'h;;marv) (Russian' tol,lll, the theorvof conform G' Method of variationsin *r. N" S' 19(61)(1946)' ntt' Math' M;; iUo*it) representsnon' MR 8-325'[24] Englishsummarv; 203-236'in"ssi"t' meanof bounded fo' "';;;;;i;i'i (Russian' 402.Goluzin,G' Estimates "::'y':! 87pp' Trav.fnrt. tntuttfi .f.ioff 18(1946), themodulu.s. MR 8-573't59l ^t:, Englishsummary) 4o3.Goluzin,G.InteriorProblems}in,Theory.ofschlichtFunctions. Transl.byT.C.Doyle,e..clj.t'".ff.,,andD.C.Spencer.office

2E

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

Wash. D.C., 1947. 138. MR of Naval Research,Navy Dept., 8-57s. [44] 4 0 4 . G o l u z i n , G ' M e t h o d o f v a r i o t i o n s i n t h e t h eN. o r l ' o f c o n f o(1947), rm Math. (Mat. Sbornik) S. 21(63) representatior"ll..Rec. 2 4 ' , 2 9 '5, 8 i 8 3 - 1 1 7 .M R 9 - 4 2 1 ' [ 9 , l 5 ' 1 9 ' 4 0 5 . G o l u z i n , G . M e t h o d - o f v a r i a t i o n s . i n c : oEnglish n f o r m a lsummary) m o p p i n g .MR tll.Mat. (Russian' Sb.. N. S. 21(194?)'l19-130'

9-42r.1241 z i 0 6 .Go l u zi n ,G.S o me co ,ler ingtheor em ' sinthetheor yofanalyticfunc [14' MR 10-21' (1948),353-3i2. 22(64) s. N. suornik tions.rnrut. Mat. Sbornik of univotent {!n:ti?:s. 17' 42' +oz. Slrrzin, G. on thecoefficients r r nirr o- tgo' i3' ,9' ,15' , , ,54' 581 ) 9 4 8 ),3 ? 3- 380' N . s.2 2 (6 4 (1 4 0 8 . G o l u z i n , G ' O n d i s t o r t i o n t h e o r e S' m s23(65) a n d t h(1948)' e c o e f353-360' ficientsof N' univalent functions'Mat' Sbornik 58' 681 , 1. 9 ,1 5 ,l '7,24' 25' 39' 54' , MR 1 0 -6 0 2'Some Izv' Akad' analyti:.*n:':ons' inequalities foi 409. Goluzin,G' 3(1949)'10i-105'(Russian' Naukfazatr'lSR 60' Ser'tvtat'tvtett' MR 13-639'[3' 17] KazakstrmmarY) 4l0.GcluzinG.on.meunvalues.Mat.SbornikN.S.25(67)(1949)' 3 0 7 -3 1 4MR - l 1 -3 3 9 '[3' t+] of the theoryo,funivalentfunctions' 411. Goluzin,G. somequestions MR 13-123 111pp' (Russian) Trudv tnlat.inst' Sieklov'2'7(1949)' Mat. sbornik for boundedfunctions. +rz. Hluzin, G. someestimates , l? ' ,20' 21' 22' ,30' MR ll- 426'[2' ,10'15' ) 9 5 0 ),7 - 18' N . s.2 6 (6 8(1 Mat' SbornikN' S' 27(69) +r:' 8}"zin' G' on tvpicallvreolfrtnctions' 15',17'-45'51' 52' 661 (1950),zot-itg'NAn rz-+qo'[3' 13', 4 l 4 . G o l u z i n , G . o n s u b o r d i n a t e u n i v aNauk lentfu n c t i oIr{oscou' ns.Trud yMat.Inst. MR SSSR'' atue' Steklov38i;;;i; ;8-7r' izdzt' 1 3 - 7 3 3I .l ] Mat. SbornikN' univarent functions. of theory the on i. Golurin, 4i5. M R l3- 63e'[15'24' 68] s. 2 8 (7 0i)i q l i l ' 3 5 1 - 35d' N' univarent iunctions.Mat' Sbornik 416. Goluzin,G. on thetheoryof , 53'58'661 , ,39' M R li 223' ig'13'15'24' (R u ssian) s.2 9 (7 1(1 ) 9 5 1 )' 4 l T . G o l u z i n , G . o n n a j o r a n t s o f s u b o r d i n a(Russian) t . e a n a lMR y t i c13-223' functions.|. 209-224' 29(1:)trqsil' S' N' Sbornik Mat.

rv, M11, mapping' in conformot method 418.hl3;ft,t31 variationat ?A',26',s81 15' tr-+s+'[9', +s\-+sa'uh' (1951)' N. s. 29(71) Sbornik

(PART I) BIBLIOCRAP!{Y OF SCHLICHT FUNCTIONS

of functions parametric representation -29QD 419. Goluzirr, G. On the (1951)'469-476'MR N' S' univalentin a ring' Mat' Sbornik 13-930.123,24i analyticfunctions' ll' of -s,ttbordinate 420. Goluzin. G. O" ^oio'otion (i951)' 593-602'MR ll-454' Ui Mat. Sbornil
tN' s'igrtl951)'72r-72:3' exal. NuutSSSR Dokladv 1 4 l, 7, 5 4 1

4 2 2 . G o l u z i i i , G . A v a r i q i i o n a i n t e r h o d i n t hSer' ethe o r y oNat'k f a n a' l y23(1952)' tic.functions, Mat' 144' Leningrad Gos' Univ ' Uc' Zap' 1 3' 1 5 ' 2 3 ' 2 4 ' 5 8 1 8 5 - 1 0 1 .f v f n f Z - f 0 7 0 '1 2 '6 ' 9 ' 61 Amer' Math' Soc' TranslationNo' 423. Gtlluzin, G' On nreanialues' ( 1 9 5 2 ) l, 0 P P ' M R 1 3 - 6 3 9 '[ 3 ] 4 2 4 . G o l u z i n , G ' G e o m e t r i c t h e o r y o f f u n c t i o n t o { - 1 ' : ^ p l e x v[4] ariable' pp' (Russian)YR'15-112' GITTL' Moscow,(1952)'S+O 438 pp' Funitiontheorie. Berlin, 1957, Geo'm-etrische G. Goluzin, 425. M P . 1 9 - 7 3 5 .[ 5 9 ] 4 2 6 . G o l u z i n , G . o n a v a r i a t i o n q l m e t h o d i n t h e t h e o r MR y o . f23A-332. onalyticfunc. (2) l8(19611',|^'4. tions,e'.,. ruru.t'.soc. Transl. g ' 1 3 , L 5, 2 3 ' 2 4 ' 5 8 1 'A t r a n s l a t i o no f 4 2 2 1 26 ,, 4 2 ? . G o l u z i n z , E . G ' o n t v p i c a l l y r e a l"17(1962)' f u n c t i o n No' s w i t7' h f 62-70' i x e d s e(Russian' condcoefUniv' Leningrad' ficient.Vestnik 15' 661 Englishsummary)MR 25-426' tl3' 4 2 8 . G o o d * u n , n . w . o n s o m e d e t e r m i n a n t s r175-192' e l a | e d t MR o p - v9-421' a l e n t f14' unc63(1948)' Soc' Math' Amer' tions.Trans' 14,16, 17,42,501 4 2 g . G o o d m a n , A . W . N o t e o n r e g i o n s o m i t t e d b y ul 0n-i 6 va l e' [n1t 8f u' 1n9c]t i o n s . 01 B u l l . A m e r ' M a t h ' S o c ' 5 5 ( 1 9 + ! D ' X l - l q g ' Y R p-valentes.c. R' desfonctions 430. Good-ar,, A. il . sur rescoefficie:ns -g}'16'10'14'17' Acad.Sci'Paris228(lg4g)'1917-1918'fufnf: 36,38.39,501 ,N. on the schwarz-christoffelrransformaiionand 431. Good*un, a. p - v a l e n t f u n c t i o n s ' T r a n s ' e * . ' . M a t h . S o c . 6 8 ( 1 96530' ),6,42't,645- 2] 2 3 . 3 6 ' ,3 8 ' ? ? ' , 4 2 '5 0 ' , M R l 1 - 5 0 8 .[ 6 , 1 0 , 1 4 , 1 5 ' t i ' n ' , 432"Goodman,A.W.Typicolly-reatlunctionswtth^lssisnedzeros.Proc. *i il-11,it''tu'17'5Il itrgsri'zig-tv.' ruru*.r.'soi' ,A,mer. boundary points- Proc. Amer. 433. Goodman, A. w. Inoccesstble

' [6' 10] NIR 14-367 Math.so". iiiqsz),742-7s0'

4 3 4 . G o o d m a n , A . W , T h e r o t u t i o n t h e o r e m f o r s t a rM l i kRe 1 u4 n -i v7a3l9e'n[ 6t f9' u' n c S o c 4 ( 1 9 5 3 ) , 2 i 8 ' 2 8 6 . M a t h . A m e r . tions.proc. 1 5 , 4 9 ,5 8 , 6 3 1

F

30

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

Amer' Math' boundedfunctions' Trans435. Goodman,A' W ' Almost 1 7 ' 1 8 ; 2 7' 3 4 1 S o c .7 8 ( l g S S l8, Z - 9 7 'M R 1 6 - 6 8 . 5U' 5 ' in the typical'lyieul and mer,omorphic 436. Goodman,A. w. Functions 92-105'MR 17-724' Soc' 81(1956)' unit circle''l-'an''Amer' Math' 66] . [ 9 , 1 3 , 1 5 , 1 7 ,2 3 ' 5 1 , curves' Uniu'olent functions and nonanalytic 437. Goodrnun, ,i.--w.10] 598-601'MR' l'9-260'[4' 6' Proc. Amer' Math' Soc' 8(1957)' .for multivalentfunctions' 43g. Goodman, A.^il-. varia'ion formulas 129-148'MR 2O-5M' [14' 16' 'r'-coc rA-rner. Math. Soc. 89(.1958), I r d'rrJ' rrrrvr

2c1"aman, pointsfor an anarytic A. w. variaiionof the branch +:g. 8)'2i7-284'MR 20-969' Math' Soc'89(195 Amer' function.ftat'' fo'-y:i::t'n'fur;ctions' *0. 3:f"aman, A' W' on variationfctrmulas MR 2u-969'124'421 285-294' 89(195d)' Soc' Trans.Amer. Mth' functions' o-fo *-u!'lu,alent 441. Good*un, A' W ' On thecritical'paints 20-969' [14' 16' MR ZIS-109. Trans.Amer.Marh.Soc.89(19Sii1, mappingonto certaincurvilinelr 442'olnd*un, '\' W' Conformal 20-26'MR 13(196C)' Univ' Nac' TucumanRett'Ser'l' polygons' 26-743.16,241 4 4 3 . G o o d , n u n , A . , w . A n a l y t i c f u n c t i o n60-64' s t h o tMR26-63' t a k e v a l u U' e s il0l naconvex Sot' t+(tgO3)' region.p'ot'nrntr' tvtattr' univalent func' On regionsomitt-'-d 'b/ 444. Good.nun,e' W', ntittt' E ' l9l g3- 88.MR l5- 579.17,18, ti o n s.Ir.ca n a d .J. Ma th.ztr q:a] 4 4 5 . G o o d m a n , A ' W ' , ; R o b e t t ' o n ' Vq i ' S ' A c l a s s oMR f n t 12-6ql u l t i v o' l[6' entfuncAmer'Math' Sot' fO(f 5D' 127-136' tions.Trans' 1 0 ,1 3 ,1 4 ,1 6 ,1 7 , 3 9 , 4 25' 0 ' 5 l l 4 4 6 .Gco d **,n .,p .,o n th e Bloch- Landauconstantfor schlichtfuncU' 191 tions.Bull'Amer'Math' Soc'S(tq+|D'234-239'l'irR6-262' ^oint*iitque, 1924.FM 50-150'[591 4i7. Goursat,E. iou* d,anolyse 4 . l s.Gra d ,A .T h e re g i o n o fvaluesoftheder iuative^ofoschlichtfunclg8-202'MR 11-503' 36(1950)' fion.Proc.Nat'Acad'Sci'u's't' functionswhich D. s. on theanaryticcontinuat.ion^of 44g.8::""^srein, ma p th e u p p e rh a l fp l aneinto' itself.J.Math.Ana!..Appl.1( 1960) ' ni-tez. MR23A-6lu'[59] theirApplications' U'; Szegti'G' ToeplitzForys-and 450. Grenander, 20-223'159lr pp'MR Univ. of Calif' Press'Berkelei tgsg'zqs i'i4"s' Trans' Amer' Math' Soc' 451. Gronwall,T. On a theor'^ ii (1912),M5-468'FM 43-321'[59i

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS (PART D

31

represent'ation'Arrn' of on conformol rema:ks Some "45-672' T' 452. Gronwall, 18' 19'221

[9' ^iu' -ts), tz-t6' FM Marh.tzl rotigr4 conforme' representation to ieformationdansla 453.Gronwall,T' i'+g-zsz'iu+o-ls:' [10'15'64' c. R. Acad.stilp"'i'"l62(1916)' conforme dansla repr\sentation 454.8l"nwall, T. sur la d,formaticn 162(1916)' C' n' ecad' Sci'Paris reitrictives' sousdescondittions : r o - r r g .F M 4 6 - 5 5 6u' 0 ' 1 5 1 th.esecond in conform'clmapping^w|rcn 4)5 Gronwall,r. o, distcrtron volue' Nar" hasan assigned coefficient i'Jlil'i *opping funciion47-324' [e'15'58'681

Proc.siiitoj,iinJoz'.Frvr Acad.

y?!p:::in theunitcircte' r' A;;;;* t'\|tt yli' tositive .i55.Gronwall, [2] gzr-zl;:fi122. FM 4s-403. Ann.of r'rutn.z':jr Ann' mappings'

andconformal of series 45?.Gron*uil,rl irm mation ' zbl3-55'[59] of Math.llir-q3zl,101-1r7 Funktionen'It''Ih' anaiytischer singutorrtatrn ire ii;;; w. , 458.Gross ' FM 46-512'[49] Math.u- P;;'tik zqtrqrll' 3-47 in der Umgebung

Ftnktionen analytischer 459. Gross,W ' Zum V"ialten 2(1918)'242 294'l59l singularerSi't't'n' Math' Z' Abbilk.onformen a*trr*)ti'robleme_de-r cinige r la" H. 460. Grtitzr.rr, 800928)'iol-ye ' FM 54-378'[15]Abbildung. LeipztgBerichte ntt"kotprobleme der konformen 461. Grdtz,,n, i7 ii'r einige gotrgjg)' 4g7-502' FM 54-378'[15] dung.ll' LeipzigBerichte bei schlichtennicht konformen verzerrung ai, u ri.'JE Grotzr.n, 462. Erweiterung einedamit"zusommenhangende -5C7'FM Abbilduttg" 503 ileticrtte 80(1928), "i'n'r ces picardschensatzes. l-riprii berschtichterkonformerAbbityber die verzer.rung -rr. Lt;;:;J:t-l schlichter Bereiche. Leipzig dung mehrfach zusamm, nniiie;ni,, 55-793'[24] verichtesitigzgl, 38-50'FM Abbildung unendlich vielfach konforme 464. Grotzrrn,'ji.--0i* z u J o m m e n h a n g e n d e r s c n t i c n ,g.richte i e r B i r e31(1929), i c h e _ m5i1-86' t e n dFM lichvieleri Haufungsrandkomponenten.j.iorit

^ur.TJ::;tf?l

Abbitkonformer beischtic-hter hberdieverzerruns

dungmehrfachzusamm'nno-ni'iaerschlic'hter'Bereiche'II'Leipl24l FM 55-7e4' zignerictrti]ituiinl'2r7-2.2r' Aboild_er ,konformen 466. Grirtzsch,H. hber ein v"rioiio)liroblemeFM 56-298' [591 251-263' dung.LeipzigBerichte82.(1930)' AbbilkonJ'ormen der. parattrtui'iiiinrorem 46.7.Grotzsch,H. zum reiche' e B r g d e n e nhiin un' nati' n-ui' i o']"u' o* ^ e dung sch''l i'i' "1'

32

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

185-200'Zbl3-14' U6' 601 LeipzigBerichte.33(1931)' bei schlichterkonformer 468. Griitzr.tt, ff' Ua') ai'' Verschiebung Berichte' (1931)' pp Leipzig Abbildung rriti-rhru Bereiche' 254-279.zbl3-261' u9, 601 konformerAbbil' H' 0i" ai' Verzirrungbeischlichter 469. Grotzsch, Bereiche'III' Leipschlichter zusammenhangeider dungmerhJ.ach 283-297'[60] zig ierichte 83(1.931)' bei schlichterkonformer 470. Grotzsch,Ft. Vori'Extemarpiotjrme Abbildungscntr,nterBereiche.Leipz\gBerichte34(1932),3-1I4.2b| 5 -6 8 .[1 9 '6 0 ] der konfornter 471. Griiizsch, Hl 1ber das Parallelschlitztheorem Abbildune"hti'h"'Bereiche'LeipzigBerichte84(1932)'15-36' zbl5-68- u9, 57,601 kcnformer ii'Oer aie Verschiebungbei schlichter ^'rnirrnrc, 472. Grotzsch,tl' 84(1932)' Berichte Bereiche:.II. Leipzig Abbitdung Zbl6-17l' [29' 60] 269-2'.78. konforrnenAbbilderschlichten H. (iberdie Geometrie 4.13. Grotzsch, Wiss'' Phys'-Math'Kl' (1933)' dung. S,t'gsUet'Preuss'Akad' 6s4-67| . Zbl 1 -3r2. I24j derschlicntenkonformen Abbil' 474. Grotzr.t, ff ' tii" aiL Geometrie V''i;s''Fhys'-Math'Kl' (l 933)' Presuss-'-Akad' Sirzgsber' dung.Il. 893-q08.zblS-319.u5' 491 der konformen i*ii v"t'hiebungsltrobleme 4'75.Grotzrcn,i'" ii" Kl' Pt'ys'-Niath' Wiss'' Abbitdung' Sitzgsber'P"u"' eUO-' (1 9 3 3 ),8 7 -1 0F0M . 5 9- 349'[24] beischlichterkonH. Die werte desDoppelverhaltnisses (1933)'87-100' 4j6. Grotzsch, Ak;;' wiss' Sitzgsber' former eaiiti"s' Preuss' zbr1-?r4.lsgl Satzes' eines Bieberbaclischen . Grotzsch,H' Verallgemeinerung 477 FM 59-351't60l ^ Math. ver. a3(r9i3),r43-^145. Jber.Deursch. g' Jber' o)r t aii k ttrfo r men-A bbil Cun F lo,che,,r 47g. Gr
480.f;;l;tl]?i%

Abbit' konformen derschtichten erdicGeometie -math'Kl' (1934)'

Preuss'atua' Wiss''Pnys' dung.Ill' Sitzgsber' 434-444.Zbl rr-313' [49] 4 x l . G l i j t z s c h , H . Z u r T h e o r i e d e r V e rHelv' s c h i e8(1936)' b u n g b 382-390' e i s c h l i cZbl hterkon. Math' Co*-t"t' Abbitdung' former 1 4 -2 6 7[6 . ,9 , 1 5 ,5 8]

B I B L I O G R A P H YO I ' S C H L I C H T

F U N C T I O N S( P A R T I )

33

einzur konflrmenAbbildung Abschotzungen Neue H' Grtrnsky, 482. u n d me h rfa ch zusam m enhangender Ber eiche,Schr .Inst.Angew . q5-t+0.zbl 5-362. [9, l5 , 22, 60,6ll g.ri. r 1(1932), Math.univ. Lemma' Math' '^'nalogazttm Schwarzschen it' EiruP,e ;i83. -" " ' Grrrr,sk;r, zbl6- 262' l37i o n n . t6 g (tq r:),190- 196' zur konformenAbbildung'Jber' 484. Grunsky,H' ZweiBen;crkurigen D e u t s c h . M a t h ' V e r ' 4 3 ( 1 9 3 3 ) ' l ' A b t ' l 4 O - 3 ' Z b obbildende l8-119'tll'15'681 ftir ylti1ht Xieffizi)nt'nibedinsungen tt' siv, Grun 465. istt%g), 29-6r. zbl 22-l5l ' meromcrpnepu,,iironcn. Math.2. [4 ,9 , 5 3 ] Abbildungendie gewisseGebiets486. Grunsky, H . iJber konforme I. Math. Z. Funktionentransformieren. inii^rntaie funktionen "ol MR 19-538'[59] (tgsl), 129-132. als ier Uniformisierungstheorie Crurdaufsabe nii, 4g?. Grunsky,H. 139(1959/60)'204-216' MR Extremalproblem'Math' Ann' . \u,49\ 22A(l)-805 4 8 8 . G r u n w a l d , G . ; T u r 6 n , P . ( J b e r d e n236-240'-FM B l o c h s c h e63-300' n S a t z .U9l ActaLitt.Sci. Sect'Sci'Math' 8(1937)' 'E' Univ.,Szeged, J' LondonMath' meansoi po*" series' Cesdro 489. Gwilliam,A' 248-253'Zbl 13-68'[3] Soc.10(1935), meqnsof power series'-ll'Proc' Londo^] a9O.Gwilliam,e' E" Cesdro zbl 13-68'[3] ^i." 40(t935),345-352' Math. so.. its. Paris,1910,FM desVoriations. 491. Hadamard, frqin, ,ui l, Calcul 4t-432.Isgl mappings-proc. Amer. Nlath' 4g2. Ha\mo,D. T. A note on convex M R 18- 411'14'9' 10' 3ll S o c.7 (1 965),423- 428' 4g3.Hamdi,o.UberstarkschiichteAbbitdungdesEinheitkreises. U n i ve rsi te d ,Istanbul.FacultedesSciences.RecueiideM em oi r es Commemorant!aPosedelaPremierePierredesNouveauxlnstituts Istanbul'(1948)'3g-M' MR 10-524'14' de Ia FacultedesSciences 17,191 494.HardY,G.H'AtheoremconcerningTaylor'sseries'Quart"I' FM 44-476'[59] Math. 44(19i3),147-160' 4 9 5 . H a r d y , G . H - ' T h e m e a n v o l u e o f t h e m o d u l u s' -FM of.ananalyticfunc269-277 45-1331' ("2) t4(1915), soc. proc.London Math. tion. v'ith series concerning +qo. Hi".ay,G.H.; Littlewood'J'E' A theorem Meddl' Kobenhavn applications to the theory of functions'- 42' 501 '7 (1 g 2 5 ),No' +, 16pp' FM 5l- 272' ll4' 17' 18' concerningCesaro 497. Hardy, G.'ff'; f-iitfewood' J' E' Theorem meansofpowerseries'Proc.LondonMath.soc.(2)36(1934)'

T

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

. 516-531.FM 60-257.[59] tg meanvstues Theoremsconcerntn 498. Harciy,G. H.; Littlewood' J' E' J' Math" Oxford Ser' of analytic or ha:monicfunctions' Quart' tzlts+t\, 221-256.MR 4-8' 13, 471 Cambridge eilya' G' Inequuliries' 499. Hardy, G'H.; Littlewoocl'J'E' Univ- Press1934,314 pp' FM 60-169' [59] 5 0 0 . H a r u k i , H . T w o t h e o r m s o n t h e u n i v a l e n t f u nMR c t i o7-287 n . P r 'o c14' 6' 622-623' Phys.-Math. Soc' Japan (3) 25(1943)' 11,15,43,681 50l.Hausdorff,F'.Mengenlehre,3rdEd.WalterdeGruyter,Berlin,

rs35.Zbt 12-203.ls9l andconvexity starlikeness, S. i. fnL ,id;i o7univalence, 502.Havinson, lzv ' connecteddomuins' of a classof antatyticfunctions-in muttiply lvIR' 233-240.(Russian) vyss. Ucebn.Zaved.Mat. (r95g),No.3(4), 2 5 - 4 0 .[ 1 ] , 1 2 , 4 3 , 6 0 ] in the tlteoryof functions. Proc. 503. Hayman, w. r. so^i inequarities 159-178'MR l0-186' tll CambridgePhil' Soc' 44(19481' in the theory of functions' Proc' Lon504. Hayman, W' K' Inequalities

MR 1l-221591 45-473' conMarh.s;- tzl sr(1949), of

in the theory functions. Tech. 505' Hayman, W. K.,Symmetriz|:ation Task Order 5' Stanford Rep. No. ll, Navy ContractN6-ORI-106 15'l7' 19'22'24'33' U n i v . ,C a l i f .( 1 9 5 0 )3, 8 p p ' M R 1 2 - 4 0 1['1 4 ' 5 0 ,6 1 , 6 5 1 of the maximum modulus of 5C6. Hayman, W' K' A characterization l15-154' origin' J' AnalyseMath' 1(1951)' functionsregulorot the MR 13-545.[59] 5 0 T . H a y m a n , W . K . . S o m e a p p l i c a t i o n s o f t h e t r a n s f155-179' i n i t e d i a VIR meterto Math' 1(1951)' the theory cf functions' J' Analyse 1 3 - 5 4 5[.9 , 1 4 , 1 5 , 1 9 ,3 3 , 6 5 , 6 8 ] 508.Hayman,W.K.Themoximummodulusondvalencyojfunctions meromorphicintheunitcircle.I.Il.ActaMath.86(1951),89-191' MR 13-546' [9' l'4] 193-25',7' with valuesin a given domain' Proc' 509. Hayman, W' K' Functions MR 14-156' U7 ' 19' 2';1 Amer. Vtattr. ioc' 3(f 952)' 428-432' 5 l 0 . H a y m a n , W . K . o n i i e v o n l i n n a ' s s e c o n d t h e o rMR e m ul6'-122'1591 ndextensions. B-end.Circ. Mat' PalermoQ\2('1953)'346-392' 5 l l . H a y n a n , W . K . L o r e g i l l e r i t c t i e s f < s t t c t l o n s u n i y a l el?n',t 42', es.C .R. 54' MR l5-516' [3' Acad. Sci. Paris 237(1953),1624-rc;5'

621 behavior of p-valent functions' 512. HaYman,W. K. The asymptotic N{R'i7-142' U4' 25'7-284' Proc. London Math. Soc. (3) 5(1955), l o , 1 7 ,3 3 ]

FUNCTIONS BIBLIOGRAPHY OF SCIJLICHT

(PART I)

35

on Func'ions (Jniformlynormalfamilites;Lectures K' jl3. Haymun,Y' Ann Arber' igg-ztz' u"r"' Mich' Press' of a comp'J u;i;;u'

function-s" ondattied of schticht '"*''ie-n11 Fi) 11 l?^:;;Xl#. ,,* '\msterdam'vol' III' Co"g"""bf lvlath' 1954'

Proc. of Int' 102-108'R'utnp'-fioo'aftoffN'V'Cto"i"gtn'H'HollandPubi' l9-4M' l44l Co', Amstt'Ju*' 1956'MR in l"lath Tracr's Funiions'Cambridge w"f-'-'Mul'tivalent Press'Cambridge' 515. Haymun, 48' Ce'r'btl;;t University -Phvs'' No' Math' ani 21- t349'1441 problems i tg sg ),l :l P P 'M R solvedond un'otuedcoefficienl Some w''K' Hayinun, 516. fo rsch l i rh 'i u n"ion' ' Sem ' "t"ittitiunctionsl( 1958) ' 264- 277 ' of univatent thetargecoefficie^nts Bounds.for ,, .?:;^::]t*lt6; 250/13(1958)'l3 Sci'Fenn'Stt' e' I' No' AtuO' functions'Ann'

't)

5rs.li;,fl,it;ii.

Prt19, functions' of univatent ,0, c.oefficients U6' 471

5e;";;;-;;4' MR 22A(2)-e64' cambrideePhil' soc' 55(le London with positirerelt-part'J' On f' functions W' Haymu", 519. lvh.th.Scc'36(1961)'35-48-zvi'it:-Zi'rt'rn2'7-6s'12'3'6'7'rs' 1 6 ,\7 ' 2 1 ,2 2 ,23' 45' 52'9.71 . functioits' limits of moduliof-on,aiytic nil'r.'on'the Haymun, 520. 26-65' [59] 143-150'MR Ann. Polot' *ltn-' 12(1962).' 5 2 l .H a yrn a n ,w .K.onr ur r r r r ir r r or lr yir ir ntto.funivar entfuncti ons ' J.LondonMath.Soc.38(19eii,v6_243.tvlR26-|209.[8,17,33, the growthof multivatent w' K'; KennedY'P' B' on ,rr.X;;iltr, MF 20-969' Math' sot litrqsg)' :l:-lal i""0"" functions'J" Math' AbbitdungcchtichterGebiete' ,rr. Hl;,r!;'ild, J' zur konforme

U6'2el tJi-tls' MR.le-401' of a 7.. 67(,res'ti' iheorycf Functions Ci:tirricat

in tn', Topics ,M. Selected 524.Heins complexiiiit'gort'RinehartandWinston'NewYork'1962' funktionen rheorieder atgebraischen und ,rr. lf3"or3,,'i?l'-*osberg,G. Kurven ilgebraische 'qn*'"al"i in" und einerVarisblen ' L59l yeipzig'1902'FM"'t33-42'7 abelsche'n*t'"i':' reellenTeil im positi!?^' mit Pote.ni'ii'n nber G. 526.Herglotz, amO' Wiss' Leipzis(1911)' Ber' Verh' il;' Einheitskreis' tzl FM 42-438' 501-511. 5 2 T . H e r s c h , J . L o n g u e u r s e x t r d m a l e s e t tMR h | o r1?-835' i e d ' e s f[59] onctions.Com. 301-337' zqtrgsil' Helvet' Math' ment.

h--*-

36

B I B L I O G R A P H YO F S C H L I C H T F U N C T I O N S

Poisson-stieltjes-Integral' 52g. Herzig, A. Die Winkelderivierteund das 37 46) Math. Z. 46ng40),129-156'MR l-213' 12' ' of Taylor series' I' 529. Herzog, F.i Piranian, G' Se/s of convergence 9 ) , 5 7 9 - 5 3M 4 'R 1 1 - 9 1 '[ 5 9 ] D u k e M a t h . J . 1 6 ( 1 9 4'G' On the univalenceof functions whose 530. Herzog, F'; Piranian, Math' Soc'2(195i)' clerivativehosa positiverealparl. Proc. Amer. 625-633.MR 13-223.12'4l of Taylor series'Il' 531. Herzog, F.; Piranian, G' Selsof convergence D u k e i d a t h . J . 2 0 ( 1 9 5 3 ) , 4 1 - 5 4M' R 1 4 - 7 3 8 '[ 5 9 1 ate Teilsummen beschriinkter Potenzreihen' 532. Heuser, p. tOi 20' 22' 6l] l4ath. Z. r9(1g35),660-662'FM 61-346' [15' 533.Hibbert,L.(Jnivalenceetautomorphiepourlespolynomesetles lonctionsentieres,Bull.Soc.Maih.France56(1938),81-154.2b1 20-140.128,32,351 Abbildung- Nachr. Kgl' 534. Hilbert, D. Z;r Tieorie cler konformen -Phys. Kl. (1909), 3|4_323. FM ces, Wiss' Gotttngen,Math. 40-132. Ls9l points' AtIj-" Form' Mat'' 535. Hille, E. A note on regular singular A s t r . , o c h F y s i k , l 9 A ( 1 9 2 5 ) 'l - 2 1 ' F M 5 1 - 3 3 5 '[ 5 9 ] Neitari. Bull. Ame,'. lvlath. 536. Hille, E. neitorks on'o paper by zeev 3 'R 1 0 - 6 9 '7 [ 2 8 ' 3 r ] S o c .5 5 ( 1 9 4 g ) , 5 5 2 - 5 5M I' II' Ginn and Co" Boston' 537 Hille, p'. anitytic Function Theory' pp" N'{R2l-1196' l44l vol. I(19591,:ifg pp'; vol' II(1962)' 496 53S.Hoh,C.Theszegoprobleminthetheoryofschlichtfuttctions.Sc\.

221 ' 119', (N.s.)z(rqis),86-91'MR 20-877 Record

der vollstandigendifferen53g. Hopf, H.; Rinow,w. Llberden Begriff tialgeometrischenFlace.Comment.Math.Helvet.3(1931)' 209-22s.Zbl 2-350. [59] bei ganzenFunktionen.Akac. 540. Hornich, H. Der schtichtheitsradius 59-65' MR 9-420' [23' 28' 13] WIss Wien. S. -B' IIa' 154(1945)' 54l.Hornich,H.ZurFragederisoliertenschlic|ttpnFunktio|l€|t.Nalath. A n n . 1 3 5 ( 1 9 5 6 1) ,8 9 - 1 9 l 'M F 2 0 - 9 6 9 '[ 2 E ] 5 4 2 . H o r n i c h , H . Z u r S t r u k t u r d e r s c h l i c h t e n F u n k i t o n e n . I . I IMR .Abh. 38-49' 176-179' 22(1958)' Hamburg Univ' Sem. Math. 20-161,664.[4' 28] 543.Hsu,T.-F.on'the.thirdcoefficientofboundedschlichtfunctions. (Chinese)MR 20-968.[22] Advancementirt Ma-th.2(|956),2,79_289. 544.Hu,Ke.onthedistortionofschlichtfunctions.Math.Sinica 4(19:+), 259-262.MR 17-142'19'15.'581 545.Huber,A.onaninequalityofFej6randRiesz.Ann.Math.(2) 63(1956),s72-587.MR 18-296'[7]

FUNCTIONS (PART T) tsitsLIOGRAPHY OF SCHLICHT

31

einer komplexen Ein Mittelwertsotz ffir Funktionen MR 546. Iiuber, H' MJ;' Helv' 21(1948)' 58-66' veranderli,n'ln"-co^ment'

onjr*

in von F-ingsebieten ii,iaivtische ^Abbitdt:nsen 54? 9(rgiil' toi-tog' MR i3-337'[59] Math' l""tto"'' Ringgebiet' Flachenin R'iemannscher Abbitdu'ngcn otrotyti"ne Uii'' ' fl 548. Huber , [s9] Helv' 27(rgfi;' 1-72' MR l4-s62' sicfi.com",;;M;t' 5 4 9 .H u ck.*u n n ,^ 'U' ' iii' einigeExtr oblemebeikonfor 200-208'MR mer z' go(tgoz)' il"irt'imalpr Abbitdung 'tn" k"*ringis' 9;;ff;,ttl:

withco;tof af1n'ction theimase cove.r'!.21 )Ir], if;::tl. MR' j(rqszJ'ss+-sgo' (chinese) 550. "rment rnruirt' in veximoge'eau?ntt'nent

2r;fri'?, tl), Pacific functions. ofstartike ,zrtt!1llt lil 551. lsions tvti zo- zq2' 16' ,24' ,291 1381- 1389-

J. Ma th .7 (1 9 57) , Proc' m-ithodfor storlikefunctions' variationot i :.e. 552. Hum*et, l'7 82-8;'Mizo-zgz' [6' 10' '?A'29'?6' Amer.Math'Soc'9(1958)' 3lfl'"mel, of starrikefunctions. the crass J .A. Extremorprobremsin -t 553. 18ee'16'24i ol'"iit ng e6 Il(l Soc' Math' Amer' roc. P 5 5 4 ' H u m m e t , r . e . T h e C r u n s k y ' i o e Proc' f f i c"y:,7:@i eAmer' n t s o f sMath' c h l i c Soc' h t f u n15' ctions. n5g;"' Univ. of Maryland'NSF-G 28-258'[4' 17' 53] no. 1, F'.b.;A; lqz-tso' MR derelli tischen.Modulfunktionen 555. Hurwitr, t. o:arlrdieAn*rnaunsFunktiontheorie'Vjschr' Naturauf einenii, a;, attgemein'en" FM 35-401'[59] '242-253' fo:sch'Ges'Zurich49(1904) p'nt''io'ntheorie'Springer'1929't59l y' 556. Hurwitz, A'iCourant' 5 5 7 .Il i e ff(Il i e v),L.Zur Theor ied|er schlichtenFunktionen.A 115-135'MRnnuatr e l' 45(1949)' L'*re 6li' F"t' Sofia (Godisnik)'Llniu' ' 58] i z-a ro . [1 5 ,2 0, 43,45'67' von G'M' Golusinilber Satzes Anwendun'-f,''n" L' (Iliev), 558. Ilieff Sci' Math' Nat' Funktionen'i'n' at"a' Buigare die schtichten 20'43'681

i', it-aq'MR i 1-92'U5' z(rs$s),N;.

5 5 9 . I l i e f f ( I l i e v ) , L ' A p p l i c a t i o n ' o f aNauk ' t h e oSSSR r e m ^(N'S') of-G'M 'Golusinon 69(1949)' equivalentfunctions' Do\l ;il' rl-92' u5' 20' 43' 681 4gl-4g4'rriR' Dokl' Akad' 't.. on finite ty;;;i un'ivalenlfunctions' 560. Ilieff (Iliev), r ur n1i- 508'[15'20' 43J N a u kssS R(N' s' ) 70( 1950) ' ;- ir ' Funkai' 'liiinnitt' der sclilichten 561. Ilieff (Iliev), L' SiitzeuU" t i o n e n ' -ii A n n u a i r e ( G o d i s n i k i U45] niu'-SofiaFac'Sci'Livrel' 46(1e50); -rsr' MR 13-832'[20'

Ftr----.

38

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

schlichtenFunktionen' 562. Ilieff (Iliev), l-. iiber die 3-symmetrischen Sci' Livre 1' 46(1950)' Anuaire tcoairt'iftl Univ' Sofia Fac' 1 6 1 - 1 6 5M . R 1 3 - 8 3 2 .1 1 7 , 3 9 ,4 3 ' 4 9 1 der 3-symmetrischenschlichten 563. Ilieff (Iliev), t-^."tii* ai, ibsc'hnit,te Funktionen.C'R.Acad.BulgarcSci.3(1950),No.1,9-12(1951). 43] (German.Russiansummary)MR l3-336' [39' der schlichtenFunktionen, die 564. Ilief (Iliev), i.-iO* die Aischnitte Annuaire (Godisnik) Univ. den kreis rr.riii- konvex abbitdpn. S o f i a F a c . S c i . L i v r e l , 4 6 ( 1 9 5 0 ) ' 1 5 3 - 1 5 9 ' M R l 3 - 8 3 2 ' UActa 0'20'431 di'eAischnitte der schlichtenFunktionen' 565. Ilief (Iliev), r.iu* 109-112'MR 13-640'[20' 45] Math. Acad' Sci' Hungar 2(1951)' univalentfunctions' Dokl' 566. Ilieff (Iliev), L. On thrie fold symmetric

9-11'MR r3-r23'Ir7' 39' 43' Akad.Naukissn N.s'i 79(1951)'

functicns. on triprysymmetric ,u^nivarent soz.lilr (Iliev),L. Theorems Doki.Akad.NauksssR(N'S;-a+1tlsz;'g-12'MR13-832'll7' 20,43,541 5 6 8 . I l i e f ( I l i e v ) , L . o n t r i p l y s y m m e t r i c u n i v a l e n t f u1n5c-tt i|o4 n. s . B u l g a r . U7,20, 2 7 _ 3 4M . R A k a d . N a u k I z * , .M a t h . I n s . , .l ( 1 9 j 3 ) , 43, 541 5 6 9 . I l i e f ( l l i e v ) , L ' A n o l y t i c a l l y n o n c o n t i n u a b l e s el(1953)' r i e s o f F35-56' aber Mat' Inst' polynomials.nulgar Alad' Na'uk Izv' M R 1 5 - 3 0 1 .[ 5 3 ] die den Einheitskreiskonvex 570. Ilief (Iliev), L. ichlichte Funktionen, abbilden.C.R.Acad.tstrlgareSci'5(1952),No.2_3,1_4(1953). MR l5-948.U0, 15,20,43,49' 641 polynomials whose coefficienrs 571. Ilief (Iliev), l" S"i" of Faber Akad. Nauk SSSR(N'S') ossumea fi'nii number if values.-Dokl. 90(1953),4gg-502'(Russian)MR 15-23' [53] univalenceof finite sums cf triply 572. llief(Iliev), t_.-ri.rorr^ on the SSSR (N'S') uiiivalent 'functions'Dokl' Akad' Nauk .,<))mmctric 43' 491 100(1953),621-622'MR 16-809' [20' 573.Ilief(Iliev),L'Ontheciifferencequotientforboundedunivalent functions.boH.Akad.NaukSSSR(N.S.)100(i955)861-862.MR \ l 6 - 8 0 9 . 1 1 5 , 2 2 ,4 9 , 6 1-bounded Sci' Univ' functions' Mtl' COll' 574. Imura. H. A n'ote'on tO8' [5' 14'22] ** Kyoto S"r. L' l'{ath' 21(1952)'245'-24E' 1l. of power series-Japan J. lvlath' 575. Itahara, T. on tne mult:ivale'ntcy 10(1933,7l-78. FM 59-326' Il4'2ol 5 T 6 . I t a h a r a , T . N o t e o t t a c e r t a i n m u l t i v a l e n t f u n c17 tion,Proc.Inp. 10-308' [14' ' 27' 50] Acad. Japan 10(1934)'5M-545' Zbl

Fl!-*

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

wlt9se-imaginarypart on the unit circle 571.lto, J. One the function Tokyo Bunrika Diag' Sect' A changes itssign 2p times' Sci' Rep' 17 23' 491 4(lg#i'), \01-i14. MR 14-34' 12,15' ' 5'l8.lto.J.Onthefunctionwhoserea.lpartontheun!-l':ti'changesits signfinitetimes'Bull.NagoyaInst.Tech.3(1951)'293-305.2b|

87-286.l4ei 5 T g . I t o , J . T h e v a r i a t i o n o f t h e s i gAmer' n o f t hMath' e r e o lSoc' p o l t89/1958)' ?fameromorphic circle' Trans' functian on the unit 50-?3 I'.'IR20-405' t9,491 probrcnt regularf-unctions'Proc' Amer' 580. Ito, J. Ttie crtefficient -of

[13'l7' 49' 5l] Math.so.. riiiq6l), 5:-60'MP'22A(2)-2094' ReineAngewandte

L'emma'J' Y"'it"'a"' Schwqrache 581. Jacobsthal, 59, 63[37] Ma th . 1 6 5 (1 9 31) lineare die durch eine gegebene 5g2. Jacobsthal,i.-'00* dii Kreise, Norske werden. Kreisabgebitdet Funktionaui ei,renkonzentrisch'ert (1954)'MR pp' 22 3, vic. Selsk.st r., Trondheim(1953),No' l 6 - 5 8 1 [. 5 9 ] 583.Jakubowski'Z.J.surlenruximumdela J . o Bull' n c t i oSoe' n n e Sr-i' lle|As-aAtr| F14' (0 = a s I) dons to famille de fonctions ' 22',301 Nc' 1, 1l pp' MR 25-796'.i17 LettresL6dr'13(1962)' Bull' Lowrer' i. iae'n'odealgebriquiet equation,!: 584. Janikov.'ski, 9 pp-'MR 25-611'l24l Soc.Sci.LetiresL6ai .lz!g6l)' No' 16' univolentes des 585. Janowski,W' Le maximumd'orgument fonctions Sect'A. 4(1950)' Ann. Univ. Mariaecuiie-stclodowska bornees. 57-lz.(French.Polishsummary)MRl3-lZ2'.U5'22'6ll 5 8 6 . J a n o w s k i , W . L e m a x i r n u m d e s c o e f f i c i e2(1955)' n t s A z a145-160' ndAldesfoncbornles'Ann' Pojcn' Math' tionsuntvalentes M R 1 ? - 5 9 8[ .1 7 ,2 2 , 3 0 1 5 S T .Ja n o w ski ,W .L.emaximumdescoelficientsBzetBsdesfonc ti ons u n i va l e n te st< - sym m 6tr iquesbor n\is.Ann.Polon.M ath. 2( 1955) ' 491 r6 1 -1 6 9(1 9 5 6i.MR l7- 598'tl7,22' 30' , 58S.Janowski,W.lemaximumdelnpatrieimoginairedesfonctions univolentesborn,ees,Ann.Polon.Math.2(1955),182_200(1956). MR 17-599.122,491 5 8 g .Ja n o w ski ,W.Sur lesfonctionsunivalentesk- symm 4911tr iq ues .Ann. 201-208(1956)'MR 17-599'122', Polon.tvtattr.2(1955); 5g0.Janowski,W.Surle:svaleursextr\malesdumoduledeladerivee d e sfo n cti o nsunivalentesbor nees' Bull.Acad.Polon.Sc i .Ser .Sc i . N i a th .A stro nom ' Phys' 6( 1958) ' 255- 259' ( Russiansum m ar y ) M R . ll5, 22, 29, 6ll 25-427 modulede ls deriveede 5g1. Janowski,w. Sur lesvaleursextr,malesdu

Y

40

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

born6es' L6dzkie Towarzystwo Naukowe' fonctions univalentes Wydawnictwo Naukowe' Prace Wydziata III, No' 53 Panstwowe 22' 61lJ L6d2, tq5g. SOPP' MR 26-62' ll5' conformal mapping' Trans' Amer' 592. Jenkins,J.A. Sime problemsin 13-341'lz4l Marh. Soc. 67(19+sj,lzt-lsO' MR differentiatsin tr,iply-connected 5g3. Jenkins, J.A.'iorrtil* quadratic l-3' MR 12-400'[59] domains.Ann. or Math' 53(1951)' J. London Math. Soc' 594. Jenkins, l.e. on a theorem o.f'spencer. - R 1 3 - 3 3 8[' 5 9 ] 2 5 ( 1 9 5 13 ) ,1 3 - 3 1 6M of Gorusin .Amer. J. Math. 595. Jenkins, J.A. on an inequariiy 4 3 '4 , 5 ' ,5 8 ] . R 1 2 - 8 1 6 '[ 9 ' 1 5 ' 1 6 ' ,2 0 ' , 7 3 ( 1 9 5 1 )1, 8 1 - 1 8 5M i'So*' prohlems in conformal 596. Jenkins, J.A. Remut'ks on 147-151'MR 13-642' mapping." Proc' Amer' Math' Soc' 3(1952)'

i60l on "Some problems in conformol 597. Jenkins, J.A. Another remark ' R 15-414' 4 ( 1 9 5 3 )9' 7 8 - 9 8 1M m a p p i n g . "P r o c ' A m e r ' M a t h ' S o c '

t5el 5 g 8 . J e n k i n s , J . A . o n v a l u e s o m i t t e d b y u n i v o l e n t f241 unction's.Amer.J' 16' 19' ' N1ath.75(1953),406-408'MR 14-96'7 ll' 599.Jenkins,J.A.Symn'elrizationresultsforsom econforrnaiinMP' l5-ll5' Il)' l7' v a r i a n t sA . m e r ' J ' M a t h ' 7 5 ( 1 9 5 3 )5' 1 0 - 5 2 2 ' 24,54,681 6 0 0 . J e n k i n s , J . A . S o m e r e s u l t s r e l a t e d t o e x t r e m a t t e n g t No' h ' C o30' nirib'to of Math' Studies theory of Riemannsurfaces'87-94'Ann' (1953)'MR 15-115'[24] PrincetonUniv' Press,Princeton'N'J' 6 0 l . J e r r k i n s , J . A . V a r i o u s r e m a r k s o n u n i v a l e n t f u n1c7t i o n s . P r o'c . ' R 1 5 - 1 1 4[' 9 ' ' 2 4 ' 2 5 ' 2 7 A m e r .M a t h . S o c '( 1 9 5 3 )5' 9 5 - 5 9 9M

zel

of the traiectories of a 602. Jenkins. J.A. Ori the local structure Soc' 5(1954)'357-362' q uariratic different ial' Proc. Amer. Math. MR 15-941.[24] (2) of Gronv'sll' Ann' of Math' 603. Jenkins, J.A. On o problem 490-504.MR 15-785'[24] , , 59(1954), J. 2l(1954)' Math. Duke kolbina. of note 6M. Jenkins,J.A. A recent

rss-r62.MR 15-694'[26]

functions. Trans. Amer' 605. Je^rkins,J.A. on Bieierlbach-Eilenberg 16-24' [l' l5 ' l'7' 341 Math Soc.Z6(1954),389-396'MR theorem' Trans' Amer' Math' 606. Jenkins,J.A. A generalcoefficient -soc.??(1954),26?-280'MR 16-232' I24l Proc. Amer' 607. Jerkins, J.A. on circularly symmetric functions.

39'49] Matt,.soc.oitqsr,620-624'MR l7-249'[13'

F T I N C T I O N S( P A R T I ) B I B L I O G R A F H YO F S C H L I C H T

41

J. LondonMath' Soc' ienkins,I.A. on u lemmaof R.Huron. 609. ""MR l7- 251'[59] 3 O(t9 5 53),8 2 -384. ,itultt in thetheoryof symmetriza60g. Jenkins,J.A. some tmiqueness i15' viR' 16-460'[59] tion. Ann Math. (2) 5i(l955)' 105 functions'Trans' J.e'7 n )i"u^"entially meanp-valent 610. Jenkins, i\4R 17-143'[?' i7' 33] Amer. Math. Soc'79(1955)'42?-428' II Trans'Amer' 6ll. Jenkins,J.A. Oi SirirrL;cih.Eitenbergfunctions 341 5 1R5 1 ' 6 - 6 8 4U' ' M a t h .S o c . 7 8 ( 1 9 5 5 ) , 5 1 0 - M Math' Soc' London of Keogh' J' 612. Jenkins,J'A" O; a result M R 18- 12f i7 ' ,221 3 1 (1 9 5 63),9 1 -399. on boundarydistortion' Trans' 613. Jenkiri", J'A' Sarnethssrems ' I'7'2?'' 621 MR 17-956 Amer.Mattr'Soc'81(1956)'477-5W' of spencer.Ann. of Math.65(1957), 614. Jenkins,J.A. on a conjecture MR 19-25'u4, 16' 19'24'33) 405-410. canonical moppingsfor multiply' 615. Jenkins, i'A' Some new MR l8-568' ao'no'fn''Ann' Math' 65(1957)'179-195' connected t60l of certainq'!l:ot-:tremal meirics' 616. Jenkins,J.A' On the existence MR 19-845'[59] Ann. of Math' 66(1957)'440-453' 6t?.Jenkins,J.e'On-acanonicalconformalmappilgofJ'L'Walsh' T r a n s . a r n . r . M a t h ' S o c ' 3 8 ( l 9 s A i ' z o z - 2 i 3 ' M R Mappings' 19-538'124'60l and Conformal Functions Univalent J.A. Jenkins, 618. (1958)'MR 20-543'I44i Springer-Verlag-Berlin functions' o"r 619. Jenkins,J.A' On certain coefficients -uniualeil AnalytlcFunctions,l59-194'PiincetonUniv'Press'Princeton' ' [9' 17',24',25'54f N.J., 1960.MR 22A(2)-1377 in conformalmapping.ll620. Jeqkins,J.A, on wirgnted ditortron ' 124,29'461 linoisl. tvtattr.4(1960t,28-37.MR 22A(l)-807coefficients' Ann' with real 621. Jenkinr,r.n.-ot) univatentfunctions [15' 19' 24'391 of Math. (zi;r(rqoo), 1-15'MR 22A(2)-964' of the trajectoriesof a 522. Jenkinr, ri. on t'n, grobatstructure J' of Math' 4(i950)' positivequoa'oti' difierential' Illinois -4}s-4r2. MR 23A-330.[59] and itsopplications. 623. Jenkins,J.A. Thegeneralcoefficienttheorem colloq. Function (Internat.. contributions to function theory T h e o ry,B ombay,l960) ' pp' Llt- Zig"I' atalnstituteofFun dam engolnuuv,'ibao.MR 26-1002.19,17, 24,25) tal Researcrr, generatcoefficierutheorem' 624. Jenkins,J.A. An extensionof the Trans.Amer.Math.Soc.g5(1960),387-407.MR22A(2)_|37,7.19, 1 7, 2 4 , 2 5 1 univolentfunctions' II' 625. jenkins. J.A. on certaincoefficientsof

---

42

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

534-545'MR 23A-52' [9' l7' Tr:ans.Amer' Math' Soc' 96(1960)' 24,25, 45,49) Canad' problemsfcr typically-realfunctions' 626. Jenkins,i.e' Some 15',23',66)

ziitz)-2093'[13', 299-304'rvrn J. Math.13(1961), 6 2 7 . J e n k i n s , J . A . o , n ' t h e s c h l i c h t B t o c h c o22' n s 341 tont.J.Math'Mech. ' certsinapplicalzi'-n+' MR 23A-332'tl5' 19', l0(1961), and theorem coefficiint 62g.Jenkinr,J.a. ihr- ,rnrrol l-g' MR 24A-371' l24l

68(1962)' tions.Bull'Amer' Math' Soc' meromorof Goodman-con'cerning 629. ienkins, J'A' On o coniecture ' MR 25-27 Math' J' 9(1962)' univoint fun''tion'' tUitf igan phic '24!-3',70. 42] [9, 13, 16' !7 ,25' tb the generaicoefficient theorent' 630. Jenkins, J.A. An uddendum 26-980't241 Trans. orn.,. Math' Soc" 107(19$\'125-l/8'yR on Riemannsur' Topologicalmethods 631. Jenki.,,, f 'n'; Mot"' M' to the theory of ps.uiohar*oni. functions. contributions faces. Riemannsurfaces.Ann.ofMath.Stud.No.30(1953),111-139. MR l5-210.[59] the levelcurves Curvefamilies n\ to11t,t7 632. Jenkins,J 'A'; Morse' M' ofapseudoha'monicfunction'"At'uMath'91(1954)'l-42'MR

' Ann' or troiectories D'F'Hvperettiptic ,rr. i:;??,1;,t]?l',spencer'

4-35'MR 12-400'[59] Math. 53(1951), o7 o clossof fundamentaline634. Jcnser.J.a.#.y. Investigation Ann. Math' qualities ln the theory-o7- anitytic functio.ns. Danish from A tianslation 2l(lgl9-20)' l-2g' FM 47-2ll' I59i' Soc' and tinstn' Bull' Amer' Ma"h' Curvature d Richar Jerrard, 635. t59l l 3 -1 1 4 'MR 23A( r ) - 4- 11' 6 7 (1 9 6 1l), Funktionen.Proc. Imp. schlichte ili,, Bemerkung Einige K. Joh, 536. zbl8- 215' UOl A ca d .l u p ' g i rg :3 ),5 6 1- 564' der (JngeradenschlichtenPoten' 637. Jch, K. iAi, aii Abschnitte [20' zbl Imp' Acad J;' iitrq::i' 407-409' "5-71' zreil^ten.Proc' ,schricht'functiorts.^P^roc. Phvsico-Math' on the ,rr. i'";itl . Theorems tf- +Og'll7' 20' 39' 43' 451 S o c.Ja p a n1 9 (1 9 3 7 l)'- 12' 4bl Phvs'-Math' 639. Joh, X. fniirms'on'rrntirit' lr,ictiois.--Il..Proc' 42] 17 ' "zbl22- 151'[16' ' 22' 24' 59i;i0 ' S o c.Ja p 'III 2 0 (1 9 3 8) Proc" Lowneroil iinil,ulontJunciions. 640. Joh, x. o, o tieorem of 4.r-M'zbl rg-27r'116'17'241 tmp.acJ' il' 14(1938)' 'schlici''1u'n"iont:III" Proc'Phvsico-Math' 641. ioh, K- ;;'';;;^s oi tgt-zog'"iol2l-143'[15'20',22'?'4'43'45' Soc-Japan21(1939), 6ll

(PART BIBLIOGRAPHY OF SCHI,ICHT FUNCTIONS

I)

& 2 , j o h , K . T h e o r e m s o n , s c h l i c h t 'MR f u n c1-308' t i o n s[6' , I Vl0' . P ri6' o c191 .Phys.-Math. Soc.Japan(l) iz'Qgqo\,329-343' on ischlicht'functions' V: 9.1-tht coefficient 643. Joh, K. Theorem's (3) 23(lg4l)'409-c23'IUR problcm.Proc'Phys'-Math'Soc'Japan 3-201.116,24,421 of p-valentfuncy. the ,,Verzerntngssatz'' 644. Joh.K.; Hukusima, on tions.Proc.pttvr.-r"r"h.Soc.Japan(3)25(1943)',377-383'MR 7 -2 8 8 [1 . 4 ,1 5,65] ib;r B'weisfiir Szegtische -Vermutung 545. Joh, K.; Takaho,hi,S' Ein 10(1934)' proc. Inpenai Acad. Japan, schlichtepolenz.,.eiien. 1 3 7 -1 3 9Z.b l g- 75.[16,17,39] rrapoing on o :!'{o^" of a sphere' 646. Jorgcnsen,V' On ionformal M R 12- 401'l27l , 137' ( Danish) e' ( 1950)l3lMa t. T i d ssr... 64T.Jorgensen,V.e,emo,t,onBloch'sthecrem.Tidsskr.B.(1952)' 15- 21.u9' 461 l o o -1 0 3MR . 643.Julia,G.ExtenLsionn-ouvellsd'unlemmedeschwarz'ActaMath' ' FM 47-212'I46i 12(rg20'),349-355 a ld \quation o'x ii'nQt {olltionetles ti6e une 649. Julia, G. Sur (3rd 39 confo'rme.Ann.Scient.6coleNorm. SUp. respr\sentotion (1922),1-28'FM 48-404'l59l series; Paris. 1930.FM 650. Juiia, G. principesGeornetrnuis'd'Analyse. s6-294.146l 6 5 l . J u n g , H . P . B c i t r i i g e z u r T h e o r i e d e r s c h l i c h t e n F u n23' k t 24' ionen.Mitt. [t7' 29, pp'M R 16- 1010' No. 52( 1955) Ma th .se m.Giessen 32,42,541 I' Proc' Japan Acad' 652. Kakehashi,T. On schlichtfunctions' MR 2l-660' [4' 28i 134-136. 35(1959), an analyticfuncripresentation,of 653. Kakeya,S. On the stor-shaped 237-240'Zbl (i932)' A' tion. Sci.ntp' iofyo Bunrika Daig' 6-120.16,20,431 part on the unit imoginary 554. Kakeya,soicii. on the-functionwhose Imp' Acad' Tokyo circle ,noni" its sigi only twice' Proc' q i s- ag. M R 8- 22' U7,49' 541 l 8 (1 9 4 2 ), functions,logarithmic 655. Kaplatr,w. on Gross,startheirem,schlicht potentialsandFourierseries'Ann'Acad'Sci'Fennicae'Ser'A'I' ' 14'621 ' pp' MR 13- 337 No' 86,( 1951)23 Ma th .-P h ys 656.Kaplatr,W.Closetoconvex"hfi,,ntfunctions'Mich'Math'J' MR 14- 966'[4' 5] 1 ,(l -g 5 2 ),169- 185. 65T.Kaplatr,W.Extensionsofthecrossstartheorem.Mich.Math.J. MR 16-232'lsgl 105-108. 2(l-954), Lectureson Finctions of a complex variable. al. et w.; 65g. Kaplan,

---

F I I.

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

i i. I

!, MR 16-1097'[59] r TheUniv. of Mich' Press'1955' I 6 5 9 . K a sj a n j u k,S " t'On a g e ner alizationofthelocallyElikesndI{ Vyss' lzv'star Maksimov' J'S' of tocatlyn-ron""inorylf' functions 1. I (1958)'No' 1(2)'103-113'(Russian) Ucebn.Zuu.O.rurutfrematita M R 2 3 A - 7 3 21- 6 , 1 01' 5 ,2 3 1 the iegulsrin an annulusandconvexin S"i-"pun'ctio'ns Kasjanjuk, 660. lzv' Vyss' Ucebn' Zaved' direction of the imaginary oxis' MR 23A-'731' (Russian) Matematiku(tqsg),NJ' e(i)' 105-110' rl r rv rn 1 2 - 7-3- 8 ,4 0 .4 1 .4 9 1 '' 1 t -e, conof convex-andstar-shoped subclasses io^' S'e" Kasjanjuk, 661. annului' lzv' Vyss' Ucebn' Za"red' .formal mappings of an MR 25-796'[6' (Russian) Matematik"iiq60l, No' 6(19)' 126-139' 1 0 ,1 5 ,1 7 , 3 5 , 6 36, 4 1 oi boundeddomains.i. Lorr662. Kenqedy,p.B. conformalmapping MR 17-ll9l ' 11' 221 don Math' s"..lrtrq 56),332-336' convex' and star-shaped 663. Keogh, F'R' io'i' inequalitiesfor

domains.J.LondonMath.Soc.2g(i9s4),|2|-|23.MR16_302.[6' 7 , 1 0 ,3 5 ] schlichtfunctions'J' London 664. Keogh,F.R' A propertyof bounded l5-862' I7'221 Math so.. zq(iqs+),rzq-:g?"MR 665.Keogh,F.R.Sometheorems0nggt|orrilalmappingofbounrled star-shopedrlomains.Proc.LondonMath.Soc.(3)9(1959)' MR 22A(l)-295'16'7' 22',231 481-491. of G'M' A'st'ingtienedform of a theorem -2. 666. Keogh,F'R'; Peterson' ittigsg)' 31-35'MR 23A-371'[59] tviener.vr"itt. Berlin,1923.FM uo* Toporogie. 667. Kerekjario,B. von vorresungen 4e-3e6.[5e] 668.Kimu.a,K'ontheunivalencyandm ultivglencyofananolytic pi'V''-Math' S6c'Japan(3) l?(1937)'241-245'FM function'p'ot' 61-293.[4, 14] Zahienfolgen'Math' Z' 22(1925)' 569. Knopp,K' Mehrfachmonotome ' 9] 7 5 -8 5 l.''M 5 1 -1 ? 8[5 F' theoryof functions'Trans' by 670. Knopp, K'-nrc'"ni' o1 tn' rqSZ' io?y?:,?Ol48-308'[59] Bagemihl.New York: DoverCo' - DoverPubl' ' Representations 67I . Kober , H.^D-ictiinoryof conformal pp' M R 14- 156'[59] In c.,N e *'v" 'i '-,N 'Y '; Ig52' 208 Poren' ier Abschnittegewisser 572. Kchori, e. tie, aie Schlich.theitl4(1931)''251-262' Zbl5-250' n' zreihen.Mem- Coll' Sci' fyoio konvexeAbbitdung'Mem' coll' sci' 6?3 I1;;3; ,lt],. U" sternigeund 10', ', 12',16',20] ,267-278'iat s-loz' l6', KvotoA l5(1932) "\

--J

{

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

45

Bedinguitg die notwendigeund' hinle'iche-1le Stern' hb:r A' Kobori, 674. p"i""':tne denK"i"'i"ei'h auf denschlichten lmp' dafur, dass Kyoto onniA't' Mem' Coll' Sci' igenbzw' O"'"'""- ni;ereich i0' r6l

6' zti-iit' zbts-362'14' Univ.A 15(1?;;", rI Mem.coli' Abbitdung. ki,rurx, rna uiiirrur^ir 451 675.Kobori,A. iwi-tzo' t9',t9l,tr'20'39' r27-r3:.'' 16(1933) ' a Kvoto Sci. -1 6 7 6 . K o b o r i , A ' Z i i i a ' i ' ' i b er'ot" r d i e -n' ) biiir s c hgl4)' n i t t eI 7d1e r86' s c izbl t l i c9h-36r' t e n P16' oten' sa' ioill t*' n.r"l ihe e zr Jap'J' ivlath'13(1e36)' Ktusse yo::o.':nzreihen' ,'k''';!" 36'631 6??.i:;;: rs''17""20" zbt\;'-;;;'-ii' o' 10'11' 12' analy4e-60. t)es iutti'oten"'di'n' famitte fonctions[6'14' 678. Kobori, A' S" to zbt2o-r42' rszrsq' r+irljsi

i'np'ecaa'rap' fiques.p'ot'

Soc' 321 -"- I^' ranrtinnr mu, multivalenfes' Proc' Phys'-Math' les Sur fonctions A' 6f9. Kobori, 3 7e' [14'15'i7' 50'65]

MR 'Su' Japan(r2;(;;;;i'"qi-nt Proc' Imp' Acad' i' fonctions-*'ttiuotLnres' A' 680.Kobori, 15'6sl 'An'evolusti
- ^ n d i ^ , , o sur < , t r lun tn th\orbme de M(Jne'-remarque

J' Math' zgO'iiii'iz-34'MR Havman'Japan

U' 14'17' 23A-'71r'

v'A' zmorovic' ty:::K",( univaknt of ctass a on *.r' 686.f;.1,11 Dopovidi;i.;;.Nu.rtur.ruin.-nsd(rqsq),1060-1063'(UkrainQ\-tozl ' ll7 ' 23' 281 ian. Russian'English'u**u'it'i-rvrn'zze in thecircle' Uspehi of uni'roirnt-yunrtion, 6g7. Kocur, M .F. on a crass Mat.Naukr'7(1962)'N"'4(l;;;;lsl-rso'(Russian)MR26-62'[4'

688.5K.1;;i?.t};]f;i2aInVo'^isierungbetiebiger^onotvtischerxul-y tqt-2to'FM 38-455'[59] Nachr.Ges'wiss'Gottineeri;itnoil der a.lgebraischen Kurven 6gg.Koeb€,p. nber die unifi'misirr"rie durchautomorpheFunktio:;';;^iimaginarersubstitutions'

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

-Phys' Kl' gruppe. Nachr. Kgl. Ges. Wiss' Gottingen' Math' (r909), 68-7.6.FM 40-468. [59] Kurven.ll. 690. ioebe, p. 1ber die Uniformisierung der algebraischen M a t h . A n n . 6 9 ( 1 9 1 0 )l ,- 8 1 . F M 4 l - 4 8 0 ' t 5 9 l 69r.Koebe, P. Zur konformen Abbildung unendlich-vielfochzusamNachr' Kgl' menhiingenderschlichterBereicheauf schlitzbereicfte' 46-546' FM -Phys' Kl' (1918)'60-71' Ges.Wiss.Gottingen.Math.

t60l

Abbildung' 692. Koebe. P. Abhandlungenzur Theorie der konformen tsereiche IV. Abbildung mehrfach zusammenhangenderschlicter 46-545' FM 305-3M. Acta Math. 4l(1918), auf Schlitzbereiche.

160l Abbilduns. derkonformen zur Theorie 693.ko.ur, p. Abhandlungen auf v. Abbildung mehrfachr,rro**.nhangender schlicterBcreiche 198-236' FM Schlitzbereiche(Fortsetzung).Math' Z' 2(1918)'

46-546. [60] Lemma und einigedamit zu'om694. Koebe,i. 1At, dusSchwarzsche der Potentialtheorie und menhangendeungleichheitsbeziehungen -2i | . I37l Funktio nentheorie. Math. z. 6(1920), 52-84. Ft:l 47

69s.K n l b i n a , L . l . C o n f o r m a l m a p p i n g s o f t h e u n ' i t c i r c l e o n n o n -

No' 5' overlopping tJomains. Vest-nik Leningradskogo Univ' (1955),37-43.(Russian)IviR 17-26' [59] conformal mapping' 696. Kolbina, L. l. some extremal prcblems in DckladyAkad.NaukSSSR(N'S')84(1952),865-868'MR14-35'

124,261

DokladY 697. Kolbina, L. l. On the theorY of univalent functions. 14-35.[9, 15, Akad. Nauk SSSR(N.S.) 84(1952)'tt27-1130.MR 581 of p-valent classes 698. Kolbina, L. l. on distortion theoremsfor certain functions.VestnikLeningradUniv'II'No'7'(1956)'71-76'IviR l 7 - 1 0 7 0 .[ 1 4 , 1. 5 ,6 5 ] Proc. Imp' '\cad' 699. Komatu, Y. Ubeireiien Satzvon Herrrt Lowner. Tokyo 16(1940),512-514.MR 2-276' [59] j'be, eine Verschiirfungdes LtiwnerschenHilfssotzes' 700. Komatu, Y. MR 7-286' 17'22'24' Froc. Imp. Acad. Tokyo 18(1942),354-359'

621

Abbllcung vott 701. Komatu, Y. (lntersuchungeniiber konforme zweifachzusgmmenhangendencebieten.Proc.Phys..Math.Soc. l-42' MR' 7-514' [591 Japan(3) 125(1943), '(Jntersuchungen i)ber koiiforme Abbildung vot't 702. Komatu, Y. Phys' -Math Soc' zweifoch zusamtnenhangendenGebieten' Proc' Japan25 (3rd series),(19r3), l-42' MR 7-514' [59]

FUNCTIONS (PART BIBLIOGRAPHY OF SCHLICHT

?03.

I)

41

und ihre analytischerFunktionen Darstellungen Einlge Y' Komatu, Acad'Tokvo

Proc'Imp' Anwendune'n 'ioittgu), oif ronfolrylduiitiuis' 10'231 ito-s+i'MR 7-287'12'

fur conA'pproximati^onsverfahren otttetnierendes Ein Y' 704. Konratu, auf einenKrcisring'Proc' ein'* Rinis'ebiete eOOitiu'n[''o" forme r1-34I' t59l by JapanAcad'liitgis)' I46-.15s'-r'ln conformal'representation cn'thetneo'yii i;;' Y Komatu, 705. Imp' Acad:Jokyo 2l(1945)' functions'I'-II' Pt;' meromorph'ic ^in- [9' 17' i9] NaP'l1-170' 259-2'77,0e46;,"i-a-is+' ttnalytischen eineiii Kreis:inge der '/06. Komatu, Y ' Darstetluttgen Abbildung f?'.!?:me ""f MR Funktionen nebstden Anwend-ungen i. vrattr.tq(tg+5),203-215' potogonoiringgebiete.l"pu" uber

rlng'Math' a c'ircutar stit-mappins conformat !'f on nt .Tfl^ri:t+ 124'60) lt:giii'iq-??' M,R10-186' Japonicae fiir konipproximationsverfahren Proc' ?0g. Koma tu,.I .'Ein a'liernierendes auf einel'Kreisring' ni1fseatete 'on'in'* "1il+sl forme Abb'l;';';; gisi, rqe-155 [60] *:

A."d.';a Japan

l-:'41' representationby y' i;;' the tr'en') of con'formal 269709. Komatu, "; Japan Acad' 2l(1945)' I' II"'it;;' meromorphicfunctions' 15'17'19'25'53]

MRii-rzo'[e' 277(rsse),iii-ia+Og4e)' Abbitdung zweifach zusam-

710.Komatu, i '- 2"; konformen lv]-y'^:-t"t' JapanAcad' ri"'[i' I' Gebiete' menhangender 2r(1945),zis'-zgs'296-307'i:i-llq'3'72-3'7'7'401-406'(1949)'

,,,. Yi:l;l6i:

'fllnoo^'ntat in thetheorvof equatio:: differentiat

conformatmapping'Proc'J;;;;;ozs(rq+q)'No'1'1-10'MR 'J;R',]Jo'^'s Kodai theorem' anda distortio'n constant ?12.l(2;,f":;jti. l5' 58] lz-il'irgjol'Ml r2-2s0'[9' doMath.Sem'Rep'(1950)' )-ippiis 9f yulttotvconnected ,ii y. confor^ot oi ?13.Komatu, i" zo-lt' rrln rl-234'I'241 JapanAcad''?6(i'5til'Ni mains.Proc' ?l4.Komatu,y.Acoefficien,proiir^'forfunct!2ns,univalentinanang-i,.MR 18-292. u6, 17, Repl'*iid6, s.m. Marh. nurus.Kodai Laurentseries' coeffilil1l' the on Y' i1s. 18,]*"1u, .! ^'!p:^('l:::'' KodaiMath'Sem'Rep'gttg';'i+;-+s'Mnig-+0a'[9'13'16't't' 5riil*"tu, comainwithconvexor Y' on conformalmappineo{a 9(1957)'105-139'MR zro. ft'f"tttlStrn' ntp' stsr-like boundary'Kodai - :a:,.^ lg-94g. [6, 10, 15, 23' 63' &l TlT.Koma,u,y.onanalyticyunciionswithpositiverealportinacircle'

h---*,

Y

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS l I I

! MR 20-665' 12'7' 181 I Kodai Math Sem.Rep' 10(1958)'64-83' l Tlg.Komatu,Y.Onanalyticfunctionswithpositiverealpartinsnon' 1 2 ' 7 2 0 6 6 5 ' t M R ) '4 - 1 m ' n u l u s . K o d aM i a t h . S e m 'R e p ' 1 0 ( 1 9 5 8 8 lT 1 8 ,4 8 1 719.Komatu,Y'onconvolutionofpowerseries.KodaiMath.Sem' ' R 2 l - 3 8 8 ' 1 2 '4 ' 6 ' 1 0 ' 4 7 1 P - e p .l 9 ( 1 9 5 8 ) 1, 4 1 - 1 4 4M

T20.Komatu,Y.,ontherongeofanalyticfunctionsw'ithpositivereol port.KodarMath.Sem'Reportsl0'(1958)'145-160'Zbl87-77'12' 7, lgl 72l.Komatu,Y'onconvolutionofLaurentseries.Proc'JapanAcad. 34(1958).649-652.IUR21-1064'12,9, 471 722.Komatu,Y'Oncoefficientproblemsforsomeparticularclassesof II (1959)'124-130'MR analyticfunctions.i{odaiMath' Sem' Rep' I 2 2 A ( 1 ) - 1 8 [. 6 , 9 , 1 0 , 2 4 ] of a circle. Kodai mappings (tnd i convex starlike On Y. 723. Komatu, I 23, 1 5 . 1 0 , 2 4 A 2 5 3 . M R [ 6 , 123-126' I Math. Sem.ReP. l3(1961), 29,641 Sugaku I 724. Komatu,Y.; Nagura, S' Theory of univalentfunctions' (1949),286-302.MR 14-1075' U5 ' 24, 68) in schli:hi mappings. 723, Komatu, Y.; Nishimiya, H. on distortion 15'46] ti K o d a i M a t h . S e m .R e p ' ( 1 9 5 0 ) ,4 7 - 5 0 'M R 1 2 - 2 5 0 '[ 1 0 ' l con' [, of multiply 726. Komatu, Y.; ozawa, M' conformul mapping t MR 8l-95' 3(1951)' Rep' necteclclomains.Kodai Math' Sein' t l3-734.[5e] 127.Konig,K.Dieers|enKoeffizientenschltchterFunktionen.Mltt. g-12' Zbl l-214' U7' 541 Math. Ges' Hambg. ?(lg'rl), Funktionentheorie. 72g. Konig, K. Einigeioeffizientenproblemausder 39, 54] 27 Tohoku tvtattr.-r.rg(i-g1), 374-379.ZblT-351. [17, ,31, Funktlonen' 729. Konig, K. Eine Bemerkung iiber urgerade schlichte ' i45ll 9-25 Zbl ' Mitt. Math. Ges. Hamburg' 7 (1934), 238-239 Riesz.Studia Math ' 730. Koos is,P . Proof of a theoremof the b'others MR 2l- 131' [59] l7(1958),295-298,. of their orthogonal 731. Korickii, G. Y. On curvotureof tevellinesond 37(79)(1955)' N.s. sb. trolectoriesin conformal mappings.Matt. ) R l 7 - 2 6 ' [ 9 , 1 0 ,3 5 1 1 0 3 - 1 1 6(.R u s s i a nM of univalentcon732. Korickii, G. 'l . ort the curvat't:e cf level curves l5(1960)'No' 5(95)' t79-182' i'arnic! !'tisps.Uspehi l\'4at'Nauk (Russian)MR 23A-330. [9, 35, 49] spezielleKlossen 733. Koritzky, G. Der satz von Heffn szeg6 fur einige 9l_98. der schlichtenFunktionen. Rec. Math. Moscou 36(1929), FM 55-791. [5, 15, 2C, 43, 45, 671

I

I r

w" (PART I) BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

,B4,Koritzky,G.|J.CurvatureoflevelcurvesinunivalentconJ.ormal (N'S') il5(1957)' 653-654' moppings. Dokl. Akad' Nauk SSSR' 9' 35' 45' 49] Sussian) MR. 19-845'[6, aie'Koeffizienten der schlichtenFunktionen' 735. [oseki, f. UAer gigsgteci), [73-197. ]viR 22^(2)-1168. Math. J. Orcaramauniv. 1.24,421 7 3 6 . K o s e k i , K . ( l b e r d i e K o e f f i z i e n t e n d e r s c h t i cMR h t e23A-330. nFunktio nen.|I. u6' 125-142. Math. J. OkayamaUniv. i0(1960/61), 24,421 p_wer.tigcnFunktionen. Math. J- okayarna i3?. Koseki, K. Llber cie 87-99.MR 23A-619' U4', 15' l; ' 34' 651 Univ. 10(1960161), der:chlichten Funktionen. Math' 733. Koseki,K. Bcitrigr rW Theorie MR 24A-495' [28] J. Okayama.Univ.l0(1960/61)'1-9' T3g.Koseki,K.UberdieKoeffizientenderschlichtenFunktionen.|I|. M a t h . l . O X a V a m a U n i v ' 1 1 ( 1 9 6 2 ) ' 2 7 - 4 2 ' M R 2 3 A - 4 2 7Math' '124'42\ ier schlichtenFunktionerr' 740. Kosekr, K. Llberdie Ableitungen 2 5 - 2 5 4 'U 7 ' 5 4 1 J . O k a y a m a . U n i v1' 1 ( 1 9 6 2 ) , 4 3 - 5 0M' R und meromorphen 'schlichten . Kosek\,K. (Jberdie Koeffiz'ientender 7,11 ll(1962)' 5l-58' MR F u n k t i o n e n .I . M a t h . J . O k a y a m au n i v ' 25-254. 19,l7 , 251 ?42.Kossler,M.EinBeitragzurTheoriederschtichtenPotenzreihen. 5 (1933)'l-7 ' Zbl'7-312' Mem. Soc. Rov' Sci' Boheme 1932No' [ 1 5 ,1 7 , 6 8 ] jber besondere Klcssenvon schlicht Abbildunsen 743. Kcissler,M. Boheme(193a)7 p' Zbl Potenzreihen.l' Mem' Soc' Roy' Sci' 1 0 - 3 6. 1U , 4'00i, ,221 pctenzreihen mit beschranktemImaginarteile' 744. tscissler,M. C.R.2-'CongresMathPaysslavesl5u-151'CasopisPraha64' -1ber ( 1 9 3 5 ) ,1 5 0 - 1 5 1F. M 6 l - 3 4 7 ' [ 5 9 ] reele charakteristiken von Patenzreihen' ?45. Kcissler, M-.(Russiansumrnary) CzechoslovakMath' J ' 4(7g)' (1954)' 274-282' M R 1 5 - 9 1 4 .[ 5 e ] condition for 746. Krasnovidova, i.S.; Rogozin, U'S' '4 sufficient problem. Uspehi univalencyoj'rn, so,Utfoi of an inverseboundary Matem.Narrt(N'S')8(1953)No'1(53)l5l-153'MR14-740't4l T4T.Kresnjakova,L.Y.ontheradiiofstarlikenessandconvexitl,for lzv' Akad' Nauk Armjan' SSR' functions i io',na'd modulus' Ser.Fiz.-Mat.Nauk14(1961)'No'4'49-55'(Russian'Armenian s u m m a r YM ) R 25-39'[3, 11, l2] bounded meon 748. Kresnjatova, L.V. Analytic functions \':h . (1961)'No' 1(20)' modulus.tzu. Vyss'Ucebn' Zaved'Matematika

F

!

I F

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

il' 28] ) 2 6 - 615' .[3' 98 -1 0 3(R . u ssi a nMR with some estim)tei'foi regtlar functions (1963)' ?49. Kresnjakova,i.v v;r;. ilceun.-zaved.Mat. bounded*roi'^odirur. Iru. ' 'J ' 1 1 ' 15' 16.'17] No . 1 (3 2 ),g 4 -g 7[3 errorfuncif univatence'o{ raclius The ' 'the F";f"Od' z\g, Kreys 750. 20-969'l28l oa(rqig)'3.63-364'r'{R /ion. Bull. e.o' iluth' Soc' errorfuncThe radi)sof inivalence^of"the 281 ' zis,E';;;;;;i Krevs 751. [10' ]3' MR 21#133' 78//89"' tion-Nume'' i"n"-1'(1g59)' the On the radiusof univalen-ce^of function J' foaa' E'! Kreyslig, 752. expz'\',expt-t';A'paciricJ'il;'q'No'l(1959)'123-l2i'Tbt'

Besset runctions' orunivatence ^or ,r,. ?:;:,:;tlltili'1.d,I ' rle'1d.iy1 ' llt-iqg' MR 22A(1)-297l28il tllinoisJ. il;;'-4(1960)' schlicht "f J. Anolyiical expressions for someextremal 754. Kronsbein, MR 4-215' Math' sot' rztig42)' 152-157' r-""J"t functions.l' coefmaximumpropertvof-thefourth MR ,rr. Pl;#lbloc*i, Nr'z' A local 128' Dtk; Math' r' t+(tq+z)'109functions' ot,'iii'nt ficient

Ann'univ' (!) l''^1tentes' movenn' ,,u. i.#','i'.'r"?']!""ncto.ns ?1 i 12(1958)' 38-M' (Polish'Rus-

Mariaecu'it-skrldowskastct' t33l MR 22A(2)-1900' siansummaries) functions'B]ull' ttnivulent ^oaut;t;f maximu^ the On J' ' Krzyz, 757 1521 (3) (i;;;t' zot-zoo'MR 17-143', Acad.polon. sci. cl. rrl functlons'Bull' oiLo'nded univalent a"iuotii' ti'' On J' 758.Krzyz, Acad.Polon.Scr.Ser.s.i.rrnutt'.Astr.Phys.6(i958),157-159. M R 2 1 - 2 ? [. 1 5 ,1 8 , 2 2 '6 l ] Ann' .759.Krzy,, J. o; lhe derivotiveof boundedp:Y!!:\!,functions' (Polish' e. iz(rg58),23-28' Univ. Marie curie-Sklooo*riu"sr.,. I s' 22' 24' 6r) ' [14' 23p'-r't'7 Russiant;;;;irnn boundetlp'valentfunctions' 760. Krzyz,J' Distortion theo"^' \oi Sect' A 12(1958)'29-38' ann. Univ. Mariae Curie-Stloit'*'tu 77' U4' rs ' 22' 24' 6r ' 551 zja-r (Polish.R;';;;;mmaries) r"rn B't'll' jo' Aoundedconvexfunctions' 761. Krzl'2,: ' irstortion theorem' Math' Astrcnorn'Phys' 8(i960)' Acad' Polcn' Sci' Ser' Sci' insert)MR 24A-153'[10' ' (Russiansummary'unUounA 625-627

tii,l?,,'r?' Nex f unctions' rr' co'r b r un o e h t I n i o t #r), , ur. : i : ?.!,! : : ", Ann.Univ.Mariaecu,ie-sxioaowskaSect.A14(1960),(Polish. 64] MR 2s-7s7' [10' l5' le' 22' Russian';;;;;itt) values'Ann' with twopresssigned 763. Krzyz,l.6lr"rr'iiiirnt Trnrtions

FUNCTIONS (PART I) BIBT-IOGRAPHYOF SCHLICHT

51

Univ.MariaeCurie-SklodowskaSect.A15(1961),57-77,(Polish. R u s s i a n s u m m a r i e s ) M R 2 5 - 4 2 7 ' U 5 ' 2 4 ' 2 9 ' 5 4 1Math' 12(1962)'

Ann' Polon' 7(,4. '- ' Krzvz,J. on "i)iirc^ "{l' y?'iel' li5, 24'681 s:-eo.MR 25-611' within the fomiQ of radiis of close-to-convexity

765.Krzyz'J. The Polon' Sci' Ser' Sci' Math' univalent functions'Bull' Acad' lv1R25-1210'[5' 12] 201-204' Astronom.pnyt' 1C(1962)' functions'Colloq' of close-to-convex 766. Krzyz,J. On'iie airnati've ' 15' 29' 641 Math. rorrqoj),r il-t+o' MR 25-1210't5 'Tefectonciccnfortnol K' Isoperimetrical 767. Krz-yz'J'; RJziszewski' Sect'A' 10(1956)' mopping.enn'Uniu' MariaeCurie-Sklodowska MR 20-289'[7' 10' (Polishand Russiansurnmaries) 49-56(1958)' schrichtfunctions.Scie.Record, ,ur. Ll,t:L H. A note on bounded Zbl40-36'll9'221 Acad.Sinica:(f qSO)'157-159' on boundedanalyticfunctions' Mem' ?69. Kubo, l. Some'h;o"*' Math' 27(1953)'235-213'MR Coll. Sci. Univ' Kyoto Ser' A' 1 5 - 2 0 81. 2 2 , 6 0 ) ., ..:^. snd canonicalslit-nnapp'ng' kernel function n"i^an f . Kubo , 770. A' Math' 28(1953)'33-40' Mem. cott' Jci' Univ' Kyoto Ser' MRl5_695.[491 T T l . K u b o , T . K i t v i n p r i n c i p l e a r t d . s o m eSer' i n e qA't tMath' a i i t i e28(1953)' sinthetheoryof Sci'Univ' Kyoto Coti' fuft*' r' functions. 29g-3r1.NlR 16-122'l59i J' univslent functionsin an unnulus' 772. Kubo,r. sj^irtrization and ' MR 15-948'Il9'221 Math. so.. iupunoitqs+)' 55-67 Sugaku of symmetrization773. Kubo, T. Theory and apprications MR 20-5M' l24l ,4'5-5i' (Japanese) 9(1957/58) diameterand sometheoremson 774. Kubo, f . U1:p"Aciict'antqtnite Math' Soc' Japan10(1958)' analyticfuntctirtnsin an o'nu'l"' J' 348-364.MR 21-6s9'U9l T T 5 . K u d r j a v c e v , A . L . o n o n a p p r o x i m a t eSer' m eFiz'-Mat' t h t l r i f o r c(1959)' btainingccnUZSSR Akad' mappings'Izv' formal lVaut No. 6, ts-{z' iRussianlMR 22A(2)-2s3't59l-.^^ equotions d.ifferential 7.76.y.\farev, p.p. on integrat,oi tir'timnl.es.t right-hondside' Uc' Zap' with variablepolttr singularityin the {591 Tomsk.Uniu"t(tq46)'35-48'(Russian) equation'Dokl' io*!"','s 77?.Kufarev,P.P. A remarkon,ni'g'ol'oi A k a d . N a u k S S S R 5 T ( | g 4 , 1 \ , e j i _ o s e . - t R u s sDokl' i a n ) MAkad' R9-421.[24] 778. Kufarev,P.P' On the theoryii 'niuot'n'-fyn:':.ons' t\t-ls+' MR 9-507' 124',491 Nauk sssR (N'S') 57(1947)'

b------

52

BIBLIOGRAPHY OF

SCHLICHT FUNCTIONS

of coynlllentarvregions' 'i{t'iis'i' p.P. conformqtTaloing on MR (Russian)' 779.Kufarev, 881-884'

N;il;si;n N's') Dokl'Akad' btemof t * ^ at regionsof-thepro3e1-3e3' r." -N"J^;'S;* o bln) o ?80. f, ffr":,!'l'.?u ir'ia'i " !,?{.,'"' 6's'l e7(1e54)' coefficients' -[,rJ3l] olil''

,r,.

Y]

tf#i;fri

romskii or coerriciens' the^probtem MR (Russian)

tuat'ruetl'iiiisssi 15-18' of extremum of investigalon ^1.'.ood certain n ,rr. li'ro"Tt'ltf:Jl'' Gos.univ i':;;

problemsintie-lneorvof"'*Iit7'ntctioni'D;tl'Akad'Nauk [e'2e] tz-to6e' olr-erj-uil sssRt*'''l'io'iiqi;l' for com' 'p'robtem 783.Kurar*, "' i;^'n """tat p l e m e n "1"]';;l*:; taryao*.oin,.Dokl.;il'Nuur.SSSR1N.S.)81(1951)' ion of Golusin's 995-998.MR 14-262.[59] extenst' p'p't St*"ttinu' N'V ' On an Dokl' Akad' ?84. Kufa"u' to doubly''oin'"t'a-rqions' m'ithod 2e'481 voriationul' *tn rr-r rs3'124'

NauksssR(N's')107(195'6)'1#ioi' of the ^u-::y:'oJ

curvatureo"l 7(1956)'i23-137' MR

P'K ' On.evltuat.ions ?85. Kulshrestha' b;;it" levelcurvesof schlicht funct'io'n;' and or 20-292.L35l of curvaluu.?!,::"'' curves in th' p.K. on measu,re ?g6. Kulshresthi, a clais"ofmeanp-volentfunctions thogona!"i;i';';;"" of 33' 35] t-: o' no* zt- itl' [3]' 9( 1958) u n i t ci rcl e 'Gu nita

T87.Kung,''io'Jt'l'1:rh^;I:'#;*^J11;;";'r";;::;;!:':{'"J' equation'Aua a'ffirential 11-r42.l24l

schlicfu fun' and coefficientsof theorems tion Di'to' r7 4 788. Kung, S' l-:"ic' MP-1?-142'lr5' '

ltrq53;'ii Math'S:nica tions'Ac.u

54,68]

o^d.. thonrpratson symmetric schlichtfuncticns'

is,54t T8e(ung tt't ilr:'J;\t-tiz ,{{{r':#i s,,'iXii

Ac

?g0.Kung,s..o,ciefficientso;',i,|*iuo},ntfunctions.ActaMath.Sini 541 8;-103'MR 17-142'u7', 4(1954), Acta Math' Sin functions-' sections,or.rritirn, 7g1. Kung, s. rn, [9' 16'20'43]

lc-(-lii' vrn li-r42' 4(i?54), ettu l''rutt''Sinica4(195 'ot-'-'t^finiii'Jt' meon 792.Kung,S- on

'{*t ,'nr,

runctions tl,;;;i'?':r?;'}'t'o' tl:!:i 3{^schticht I 19-738' zzg-z+e'MR

tti' s"#"iiigssi' theorems' Distoriion 1 7 , 4 2 , 4 9 '5 4 ' 6 8 1

BIBLIOGRAPHY

OF SCHLICHT FUNCTIONS

(PART I)

53

lll' Acta Math' schlicht functions' coefficientasthe lf ?94. Kung, S' Ott Sinica6(1956),4g0-49g.(Chinese.Englishsummary)MR20-544. II' Acta Math' l4?.1 schlicht functions' ttf coeificients the ?9:. Kung, S' Ort Sinica6(1956)'115-125'(Chinese'Englishsummarv)MRi8-121' conforme' U7, 49.l. -. o..- .,a. nnn
r-:7st7' 4et Tk;':i',i;;3;:;B-';rll^n osaka function' ana'tvtic ", I*J1T,:^:;; ,;; ii'io'u ?':t:i";;;'ied re7.Kuramo.hi zbt' 48-3re'122], it:-tno' u';i'il" ,' Marh.

'"'iii;,if:::,,";tf irrii,.'ix:i,:i:;::lry:,T:::",:f&

I ;f;;;ri;"i:::"l!:i'Xit:t+tW.trf K:|{i; Kuroda, 7e8.

' Derermino",o'lu7ri,'inr."p"f.f ' nftua' NaukSSSR 799.Kuz'mina'G'V qnalYtical-J, a cerain classof

t431 ,'i 20-161' ttrli.iitil ii-is+' r"rR of unintence-of 1N.s.)

i ;i"li"J\t'\ii',"tiz-zz ,* llU;+:,?l;,::,^;i' :!,i;::i\[i:'3[ functions' rr.ln'zza(z)-1629'^143, - ..^-,nn theorems for univalent MR

(Russian) zs-31 Kuz'mll;f 801. i,giit, X,^j;'i!ji'.9ii:5.;"t; Z,A-254' llgl

Abt' ' '-)^liifschen Prinzip' Mitt' Georg'

MR transr) German 802Kwess.$1,l rn""i"'. ,?;rffif,ii,";;7:;;'; univalentes' 3 - 7 8 'U l th\orie desfonctions o'^l: Contribution 803. Lad, S' 12-19' FYs'62(1936)' casoPist;:'il' i" ^t'n:ichter FunHionen' Beitriige K' 1 7 't e ' 2 5 ' 2 7 ' 804. Ladegast' ""'iJL"l' i l - " i ' ; - ; ; ' [ e ' 1 3 '1 5 '

1 's - ] 5 ? M a t hz' ' 5 8 ( 1 e 5r3, 1

58,67'.681 3 1 , 3 9 , 4 3 , 4 5 ,5 4 ,

'n fur die bienqhe

j;i,I";i;r';:':t^::f.*:#'itin'ii'zgz-zg *"i:,'i!,'iri*;, t34l ZZntZ)-2094' (Chinese'German'u**u'oi-ft'fn s 0 6 . L a i , w . o n a c o n j e c t u r r : i o ' ; ; ; ; ; ; i " r atun t m zo-217 i s t b o u' nl34l dedfutic-

t '1'nu';'''f3-iios' Sinica tions'sci'

191 8 0 7 . L a n d a u ' E ' Z u m K o e-lq'L'FM b ' 1 ' , i ' n V48-406' e r z ' e r[9' run gssatz'F.'C'CIrc'Mat' lO'' Jber' 46(1922)' Palermo' ua" sc'htkhtiAbbildung' 808. Landau'E' Einige!':ry::i''nsrcn

z 30(re2e), ffil,n o Mu"ii{rn,7tZ^71,L:oj^1,fti}ill"^::^t' t'!.':: Uber E'

809' Landau' 6 3 5 - 6 3 8F ' M s 5 - 1 8 7 '[ 4 2 ]

5'.--**

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

g10. Landau, E. i.iber die Blochsche Konstante und zwei verwandte Math, 2.30(|929), 608-634.FM 55-770.[19] Weltkonstanten. neuerErgebnisse 811. Landau, E. Darstellungund Begrundungeiniger ' 1929 I59l der funktionen Theorie- F,d. 2, Berlin, gl2. Landau, E. jbe, ungerode schlichte Funktionen. Math. Z' 37(1933),33-35. Zbl. 6'211. 116,17, 45, 521 Trav' 813. Landau, E. Ausgewiihlte Kapitel der Funktionentheorie' 23-68. Inst. Math. Tbifisi (Trudy Tbiliss. Mat. Insr.) 8(1940), (German.Russiansummary)MR 3-78' [19] iemma' i' 814. Landau, E.; Valiron, G. A deductionfrcm Schworz's London Math. Soc. 4(1929),162-163'FM 55-769' l37l connected 815. Landau, H. J. On canonicolconformol mopsof multiply 22A(2)MR domoins Trans' Amer. Math' Soc' 99(1961)' 1-20' 208e. [60] for multi816. Landau, H. J.; Osserman,R. Somedistortiontheorems MR vorcntmoppings-Proc' Amer' Math' Soc' 10(1959)'87-91' 2l-660. ll4, 491 of Riemann 817. Landau, H. J.; Osserman,R. On onalyticmappings surfaces.J.d'AnalyseMath.T(|g5g/1960),249-279.MR23A_52.

l5el

map818. Lavrentieff (Lavre^rtiev),M. A. On the theory of confcrrnal ping. Trav. Inst. Phys. -Math' Stekloff Sect' Math" Leningrad' No. 5(1934\, 129-245.l"M 60-1026' l59l glg. Lavrentieff (Lavrentiev),M. A. Sur quelquespropri6t6sdesfonctionsunivalentes.C.R.Acad.URSSl(1935),2-4'Zbl12-214'1591 propri6t6sdesfonc820. Lavrentieff (Lavrentiev),M. A. Srtr quelques tionsunivalintes.Rec.Math. MoscouN' S. 1(1936),815-8M'Zbl

t 6 - 2 r 7U . l

des fonction's 821. Lavrentieff (Lavrentiev),M. A. Sur la continuit| 215-217' Zbl 4(1936), univolentes.C. R. Acad. Sci. URSS N. S. 16-169.l22,60l Su'"Erelques --822. Lat'rentieff (L,avrenticv),M. A'; Chepeleff' V' M' propri6t6s dis fonctions univalentes.Mat' Sb. 44(1937),fl9-326'

zbt r7-r73.lr9l

einen Ostro823. Lavrcntieff (Lavrentiev),M' A'; Kwasslava'D' Uber 17l-174' wskischensalz.Georg.Abt. Akad. wiss., ussR l(1940)' MR 2-83. [5e] problems in con' 824. Lebedev,N . i. O, someestimatssand extremal StateUniv" l95l' [241 formal mapping. Dissertation,Leningrad mapping' 825. Lebedev, N. A,-.The method oJ'variationson confttrmal Dokl.Akad.NaukSSSR(N.S.)76(1q51),25_27.MR12-49|.|24)

rr (PART I) BIBLIOGRAPHY OF SCHT.ICHTFUNCTIONS

univalent estimates ior functionsregularand 826. Lebedev,N' A' Some Amer' l'3-21' No: I 10(1955)' in a circle.V.,tnit LeningradUniv' -5gg' l7 U5' 22' 24'29'61' 681 Math.Soc.Transl' (2)22'59-80'MR 8 2 7 .L e b e cl e v,N .A' Onpur cntetr icr e:lii' esent4t' n1:!f::' tions r egul ar 103(1955)' (N'S't in o 'ing'Doki'nraA' NaukSSSR ond univalent MP-l?-3s6.1241 767-768. , expresston region fo: ifaioriztng A. N. :h, g2g.I ebedev, Univ' Leningrad ,(z),^/f(zyl in the.iorr s. vestnik 1 : lnlz^f ' 43-57 (2)'22' Nnl g' t;-^' Amer' Math' Soc Transl' 10(1955), 2+ ,2- o,68) 'A.'on MR l ? -2 4 8 .[15, o circle the theoryof conformalmappingsof g2g. Lebede./,N. Akad' t{auk SSSR(N'S') onrc non-overlappingregions'bokl' MR 17-250'[26] :s:-jjs' fRussian) 1c3(1955), 8 3 0 .L e b e d e v,N .A.onthedomainsofvaluesofo.ger .tlinfunc ti onal i n iomains'Dokl' Akad' NaukSSSR tlrcproblemo1non-overlopping 'lr9'24'26'291 19-9sl

MR (Russian) rrstrgizj,iozo-roz:' (N.S.) the

problem of nonprinciple in 831. Lebedev, N' A' The area overlappingregions'sovietMath'-Dokl'1(1960)Nc'2'640-644' MR 22A(2)-1896.13,271 of the area principle to non832. Leberl.u, N' t' )n aiplication overlappingdomcins.TrudyMat.tnit.Steklov.60(1961),2||-23]^. (Russian)MR 24A-254' t3' 26' 2711 of certoinc/asses g33. Lebedev,N. A.; Milin, t. tvt. on the coefficients (Mat' Sb) N' S' 24(1949)' of analytic functions' Rcc' Iv1ath'

68] Vrri rr-o+0' [3, 15' l7 ' 34' 42',54', 249-262. of certainclasses coefficients g34. Lebecev,N. A.; Milin, I. M. on the ' sssR 6'7(1949\,221-223 of analyticfrnitionr. Dokl. Akad. Nauk 68] MR I l-339. [3, 15, 16,l'l , 34' 42' 54', o.fcertainclasses g35. Lebedev,N. A.; Milin, I. I\,1.on ine coef-ficients 28(?0)(1951)'359-400'MR of aitalyticfunctions'Mat'lb' G'r'S') 1 3 -6 4 0[3 . , 15, 16,17,34, 42' 68] G' A' A methodof obtoiningo cer836. Lebedev,N. A'; Sogomonova' t u i n k i n d o f e s t i m a t e f o r T u n L c t i c n " ' g u l a r i n t h e c15(1960)' ircle'Vestnik rj-rq' Addendum 13' No' 14(1i59)' uniu' Leningrad tll MR 22A(2)-1376' No. 13, f SZ.in"'ian' Englishsummary) bounded with tnapping 837. Lehto,C. On the distortionof conformd A l(1952),No. 124, Ser. boundaryrotation.Ann.Acai. Sci.Fenn. 14PP.MR 14-743'[59] Math' g3g.Lehto,G.A mojorantprinciplein the historyof funcrions' , 17' MR 15- 115'Ul S ca n dl.(1 953) 5oJ^rro*orphic functionsin the g39. Lehto. G. Thesphericalderivativle

t+

-__

Y

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

Comment' Math' Helv' neighborhoodof an isolated^singularity'

[46] jl(iqsq), rs6-20s'MR 21-1063'

mero' L Bouniary behsviorond normal 840. Lehto, C.; Virtanen'K' 19-403' t59l gli(tgsl)' 47-65'MR morphictu"'iio"'Acta Math' funcI' On theiehoviourof meromorphic 841. Lehto,C'; Vi.iuntn,K' f i o n si n th e n e i g h b o u rh o o dofanislogtedsingular ity.Ann.Acad. 240'9pp' MR 19-404't59l No' (1957)' I' A' Ser' Fenn. Sci. Einheitdenschlichi'i eAaiUungendes 842. Levin, v. n'^"t"ng 'u 68- 70'U7l s k r ei seJb s. e r'D ' M' V ' 4 2 (1 933) ' dershclichten tioefJizientenpro-blem g43. Levin, y . EineE)irrruns zum lo-Tl FlvI51-367'u7l Funktronenil;' ; I'4' v' 42(1933)' der schlichten Koeffizientenoryble.yt 844. Levin, v. nii nrirrog ,u^

Funktioner.-Mil'i'zs(tgzt/;;)'306-3lr'zbr8-119'lr7'42' 45,49,521 r.-rc:-:^ r Klassenvon etntS( g45. Levin, v. jber die Koeffizientensummen t43' t59l

56s-^590: Mutn'Z' 38(rs34)' I|1^9o, Potenzreih'n'

84(,.Levin,Y.Someremarksontheco e f f i c i e n t s o f s c h l i [3',6', c h t f u10', ncns. q61-+ao''zbll2-l7l' ! ruru,t.so.. 39(193;), proc. l-onoo"n I 54'681 1 5 , 1 7 ,l g , 2 7 , 3 6 , 4 2 , 4 5 ' 5 2 ' i951 Pa'is' II proOlimesConcretsd;'lnity" Fonctionelle' 847. Levy, p' I ( S e c o n d t O i t i o t t f L e c o n s d ' A n a l y s e F o n c t i o n e l l e ' P a r i s ' 1 9 2 2 j ' tt I

deschitd th,orimes sur tes y.113;3T"1]? re.morques . euetques 848. Ann' Ijniv' Mariae univalenfes. relatifsa ,r'r'Jori de'fonctions (1957)'MR 19-738'[4' Sec'Ag(tq;s)' 149-155 Curie-sklodowska' de schild sur resth'eorbmes g4g. r.'**a1o2Jrr.i,z. Nouveilesremarques d'une uiivalentes(D,monstrotion relatifso uni ,toue de fonctionts sect' Univ. Mariaecuric-Skiodowskahypothiseir-s.iital .A.r,n. 20-292' MR summaries) (Polish'Russian (1958)' A 10(1956),81-94

de schitd th\orDmes sur tes reniarques ' Quetques f3;1,1i'l;'ll'' 850. )'*otenles' Ann' Univ' Mariae

t

I

relatifsa 'ni irto"-' de'fonctio's (1957).(Polish'Russcct.A q(iqjs), 149-155 curie-sklodowska 1 9 -7 3 8'14' ,17' tt'.3' ) ,^ ^,. s i a nsu mma ri e s)MR de fonctions ciasses |rd.enir|6de ce,ta:ne^s -\ur Z' 851. Lewandowsk!, u n i v a l e n r e s . | . A r u i . U r i i v . . r " t - i u . C u r i eMR - S k24A-37' l o d o w s[5' k a16] Sect.A 131-146'(Polish'Rt;;i;; t"mmaries) 12(1958), g 5 2 . L e w a n d o w ski ,z.su rrrrtr *r r r tor r esdefonctionsun' ivalentesinBull. Acad.Polon.Sci. -iii-'es' w."R;;;sinski. .t par P.Montel troduites (Russiansummary) MR Math. Astr' Phys' 7(1959)' 2l-l\94. [15, 19,39,' 42' 6Ei

dr F U N C T I O N S( P A R T I ) B I B L I O G R A P H YO F S C H L I C H T

univalentes Z' Sur certain-esclassesde fonctions 853. Lewandowski, d a n s d e c e r c l e , - u n i t i . A n n . U n i v . M a r i a e - C u r MR i e S k22A(2\-DA0' lodowskaSect.A

summaries)' r rs-ize' ipoti't''Russian l3(1959), ., [ 6 ,1 5 ,t 9 , 3 9 ,4 2 , 6 3 1 de fonctions c/csses certaine.s

g54. Lewandowskl,i'. i* l,identit|-de Sect.A ir,Ann. Liniv. Mariae curie-sklodowska univolentes. 11] t+(tqoo),19-46.MR 28-44'[5' holomorphes g55. Lewandowsxi,z . sur lesntaioraitesdesfonctions scct. Curie.-Sklodowska Nlariae dansIe rrrrln'\e i t Ann. Univ. 2663. N{ R [], 15] sunr nar ies) A 1 5 (1 9 6 15),_ li. ( polish.Russian subordination.Ann' g56. Lewandowski,z. starlike_majorantsand Univ.Mariae-SklodowskaSect.Al5(1961),,79_84.(Polish.RusMR 25-427'[1' 6] siansummaries) ring. univalintfunctionson_ocircular 857. Li, E. P. on tie theoryof 15_516. MR 4,75_471. D o kl . A ka d . Nout sssn N.S.) 92( i953) ,

Dokr.Aklg: onq circutarring. rear func-tions o^ typicary gsg.Lrl e10tr. M R 1 5 - 5 1 6 [' i 3 ' 1 5 ' 2 3 ' 6 6 ]

699-iC2' N a u k S S S R( N ' S ' ) 9 2 ( 1 9 5 3 ) ' M-' S' Meromorphic close-to-convex 859. Libera, R' i't ioUtttson' 2 4 A - 3 7 0 '[ 4 ' M a t h J ' 8 { 1 9 6 1 )1' 6 5 - t 7 5 'M R functions.n4itftOun 5 , 9 , 1 0 , 1 7 , 2 5 ,3 8 , 3 9 ] 3 6 0 . L i n d e l d f , E . M e m o i r e s u r c e r t a i n e spropri6t6s i n e g t i t \ s dnouvelles . a n s l a t hde ^ oces riedes et sur quelques fonctions mtonogines Acta Soc' d'un point iingulier essentiel' fonctionsaans tZ voisinage S c i .F e n n .3 5 ( 1 9 0 8 )N, o ' 7 ' [ 5 9 ] Amer. Math. Mon. g6l. Linis, v. xor, fn univarentfunctions. . R l6-809' [39] 6 2 ( 1 9 5 5 )1, 0 e - 1 1 0M Proc' inequalitieiln-tnt thecryof functions' On g62. Littlewood,J.8.. ' 5l-247 13' 421 481-519:'lY London Math' Soc' (2)' 23(1925)' of schlichtfunction;' Quart' 863. Little*ooa, J.' ;. O; lhe coeffic'ients 16' l7 ' 42' 45' 521 J. Math. qir-91[], v^-20' zbl 18-261'U' the Tieory of Functiorls' Oxford 864. Littlewood, J' E' Lectu"' on 6-261' l44l Univ. P.ers, 19M,243 pp' MR odd schlichtfuncg65. Little*ooo,'r.-r,.;'palev,R. E. A proof that an Soc' 7(1932)' Math' f' london tion hasbotmded coefficients' 1 6 7 - 9Z . bl 5-18'117,45,521 8 6 6 . L i u , L i - C h u a n . S o m e i n e q u a l i t i e s d e r i v e d f r o m fSinica u n d a m7(1957)' entallentActa Math' schlicht fun'ctions' mo concerning l'7 '22'25 '3Ol English'umma'y; MR 2l-25'' lg ' 313'326.(Chinese' in th.eunit circle. Acta 867. Liu, Li_ch;;;. Bounied schrichtfunctions (Cnint"' English summarv) MR Math. Sinica 7(1957)' 439-450' 2 l - 2 6 . I 1 5 , 2 2 , 2 4 ,6 1 7

il-T'

-

Y

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

Potenzreihen.Monatshefte 868. Lochs, G. Zur Abschutzungschlichter 191 F . M a t h . 3 8 ( 1 9 3 1 )3, 7 7 - 3 8 0F' M 5 7 - 4 0 3 'U 7 ' of Hadamard ,E' On some compositions 'analytic 869. Loewner, C.; Netanyahu Math' Soc' fu-nctions' Bull' Amer' rype in ctosre,of Lowner' also See 42' 47]' 65(1959),284-2S6'MR 21-1350'[16' 23' S T 0 . L o h i n , I . F . R e m a r k s o n e s t i o m t e s f o r r e g u l a r f u - n c1t5! 1' ,1n7s'',3M4a1t ' S b o r 10' n i k N . S . 2 4 ( 6 ; )( 1 9 4 9 )u, 9 - 2 6 2 ' M R l 1 - 3 3 9 ' U ' g71. Lohwater, A l'. rne ixceptionalvaluesof meromorphicfunctions. Colloq'Math.7(1959),89-93'MR22A(1)-455'[591 mapping of o Jordan 872. Lohwater, A. J.; Piranian, G' Conformal regionwhoseboundaryhaspositivetwo.dimensionalmeasure. 14-262' 162l Michigan Math. J ' l, (1942)' 1-4' MR g73. Lohwater,A. J.; pi:anian, G. On the derivativeof a univalentfunction.Proc.Amer.Math.Soc.4(1953),591_594.\4R15_ ||4.|62] W' The derivativeof a 874. Lohwater, A. J'; Piranian' G'; Rudin' schlichtfunciton.Math.Scand.3(1955),103-106.MR17_249[4,62] examplein conformal mapping' 875. Lohwater, A. J.; Seidel, N' An MR 9-420' [62] Duke Math. J. l-5(1948),137-143' of w" * pw = 0' Pac' J' 875. London, D. On thterrio, of the solution N4ath.12(1962),979-e9r'[4' 31] modutus of n-volencefor analytic 877. Loomis, L. H,.,The radius and functionswhosefirstn_|derivativesvanish atapomt,Bull.Amer. ' R l-308' [4' 14' 19'72'37'431 M a t h . S o . . + ( f q a 0 ) , 4 9 6 - 5 0 1M 8Ts.Loomis,L.H.Thedecompositionofmeromorphicfunctionsinto rationalfunctionsofunivolentfunctions.Trans.Amer.Math.Soc. 5 0 ( 1 9 4 1 )l ,- 1 4 , M R 3 - 7 8 ' [ 5 9 ] 879.Loomis,L'H.Onaninequalityofseideland\ltllsh'Bull'Amer' 221 ' lvlath. Soc. 48(1942),908-911' MR 5-37 ll4' die Verzerrungbei konformen 880. Lowner, K. IJnters'uchungeni)ber < l. Leipzig Berichte Abbirdungen des Einheitskreiseslzl 6 9 ( 1 9 1 7 )8,9 - 1 0 6 .I ' M 4 6 - i 5 6 ' U 5 l Abbiidung des ggl. Liiwner, K. 1be:rExtremumsdtie iei der konforrnen 65-17'FM 17-325' Ausseren desEinheitkreises'Math' Z' 3(lglg)' [ 9 , 1 0 , 1 5 , 1 9 ,2 7 , 5 8 ,& l Abbildungen gg2. L6wner, K. rJntrirrrhungen i)berschrichtekonforme 49-714' I' N1ath'Ann' 89(1932)'103-l2l' FM desEinheitskreises'

u 5 , 1 7 ,2 3 , 2 4 , 4 2 1 rotationin theunitcircle' gg3.Lozovit*, v. c. Finctionswithbounded Do p o vi d i A ka d .N a u kUkr ainRSR( 1960) ,1584-20' 1588.( 231 Ukr ainian. ' 14' 17' 23A-177 gngfith MR summaries) *nJ Russian in the gg4. Lozovik,v. c.bn o classof functionswhichare univalent

-4

FUNCTIONS BIBLIOGF.APHYOF SCHLICTIT

(P'\RT D

59

Zaved'Matematika(1963)' . (Russian)Izv' Vyss' Ucebn' unit ci,,;/e 23' 641

U0' 15' 17' No. 2(33),ol-ig' Mn 26-9-80' if thtefunction exp z'\'o rodiuso; unr'otoni' ' te ' ig' MR 22A- i629'l28l 885. Luke, Y. L' fhe e xp (-f')4 r i tu nl.' ' Math 3( i96i) ' functionsin dissertations on univ'alent results 886. Lye, Su-cin'Some se"tion of the deportmentof written by studentsin the anals:ts;is mathematicsi-ntitei'{orth.WestUniversity.Advancementin}"{ath. MR 20-1074'l$l (Chinese) 3(1957),325-334' ,iot, derivitiie hasq positivereal gg7. MacG:egor,T. H. Funciions MR 25-797'll' part.Tran ' A*;;' Math' Soc'1C4(1962't'532-537' , ,411561 lg' ,20' 21' to , t2 ,15, 17,- 1.8' 2, 4, 5, 8 8 8 . M a c G"r e g o r ' r . r r . C o e f f i c i e n t eMs R tim a t 734' e s f o[6' r s9' t al0' r l i kl'e7' m36' applngs. 2710( 1963) ' 277ZSL J' Ma th ' Mi ch .

3r;;:3;!!;rit].H. of functions for srartike of convexitv rcli1s rhe 88r. MR 27-60'[2' Soc'14(1963)'71-76'

order1/2' Pioc'Rrnt'' Idath' 6, 10, 11- 12,23, 431 analytic rodiusof univat'!:t^:! certuin 890. MacGregor"T' i{' The MR p;;..--Amer. Math. Soc. r4(r963), 5t4-s20. functions. "76-1210. 12,4, 6' 10, I 1' 121 unalytic radiusof univalen''':^o/'"'tain The i{' i' MacGregor, 891. 521-524'MR 14(1963)' tt. proc. Amer. tutat'. Soc. functions. " 2 6 - 1 2 1 1 . 1 2 , 4 ,160, ,l 1 ' 1 2 1 8 9 2 . N { a c l n t y r e , A . J . T w o t h e o r e m s o n s c h17' l i c19' h t J68] unctioits'J.London 13- 2' 7r[15' ' Ma th .so .. i Jti oS6) ,7- r l' zbl 536-540' 2.44(1938), th'eorem.vrattr. 8g3.Mactntvre,i.'j. oi' uocit's zbl 19-419.u9l '\N inequalities W' ' Someelementary Rogosinskl' i'; 894. NIaclntvr.,'A' 1-3' MR NotesNo. 35(1945), irtfunciton';'r;;y.uiinuurgtr ruru,tr.

in the Probtems w' w ' Extrly.um ,rr. filil;,|1]., o. i.; Rososinski, MR Math' 82(1950)'275-325'

Acta theory of analyticfunctions' 12-89.[59] analytic problems in certarnc:hssesof 896. Maksimov, Y' D' Extremal 1041-1044' Nuak SSSR0'l'S') 100(1955)' functions''Oofti'Akad' 15 ( R u s s i a nf)' A n f O - S f O ' [ 5 ' 6 ' 1 0 ' ' 2 3 ' 6 3 ' ' ' 6 4 ] " e-starlikemultilocally y. gg7. Maksimov, D. on locatly'r-ronirr and 965t.tuut.SSSR(N.S) 103(1955)' valent\unliton,,. Dokl. Akad. y] ' 0 ' 1 1 ' 1 2 ' , 1 5 ' , 2 3 . ' 6 3 'certain 9 6 7 .M R 1 7 - 3 5 7 ' [ 5 , 6 1 of classes of ggg. Maksimov, y. D. Boundsfoitii'rortticients Nuuft SSSR110(1956)'507-510' analvtictun'iiin'' Dokl' etui'

-.-.-

-r I i

60

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

38] ' ' 6 ' 10'17' 36' ( R u ssi a nZ)b l 7 4 -5 6[5 convex structuralformulafor of Y';:E";;nsion -tie Maksimov, 899. circularregion'Dokl' multipty"ioiected a Transl' ni,I'nr'to univalent 136(di;' 284-287-"(Russian( Akad. Nauk $;* (N's') 601 vrn zze(z)-1376'[23' SovietMath. :;;'kl''t' 55-58' potiioi'iott' Canad'Math' Bull' M' A' 7''-i"n"lity for -eftie-l), 900. '"" Malik, os-eg' MR 26-742'[591 univolentes' '3y1':ou" sur lesfoncfions S' Quetque' Mandelbrojt, 901. 'zitg-zrc[3'13'l?' 3e'

iii-zoo fi' s"setro:+l' Bull.Sci.ruruti' c' R' conforme' repr\sentation la sur R' A' tr. fi;i.lJenko, zbrrr-26r'l'tl otuJ'sti' ussnottqisi'287-2s0' of (Dokladv) prcblems in the theory

I

i i I

l I

I I i

n' Some extrema'l 903. Marchenko,-e' u n i v l l e n t f u n ' ' t ' i o n ' ' L e n i n g r a d - 5 " t ' U " i " ' 421 IJc'Zap'144Ser'Mat'

tz-to6e' 116' Nauk z3lss:;;'\{i-isg' t"tn )-'n'o"* of Lusin'DukeMath' i.; zrr*u1g,.| 904.Marcinr.i.*rJl, [59] qti-+ss' zbr' 19-420' J. 4(1938), in a como-fo polynomial the ieros o! io'"i'"i't'! tut' 905.Mard.n, (1949)'MR 11- 10I' iso'-l ;;;";vt s"t' Ma'-'h' p lexvariabl' n*-t'' t59l .. . , ^^^^-s ot tnisibftte d'une fonct;cn et troisibme second " lesd0riv6es Sur F' Marty, 906. R. Acad. Sci. Paris dals;"';:;;,-unit6. c. univulente holomorphe 10'17'42-'s4'681

us' ts4(ts32)-;ff-iti0' zbt 4-261' a' MacLaurind'unefonc'o"'ttiti'nrc a" e ' iu' t' module Zbl

907.Martv, C.R. Acad.#i.;;;i; tionunival,nt,.

iqg(rql+),1569-1571l.

Pr' Ak' ';i:; Sitzsber' Funktionen' yolylltichte ,"1,:T;J';'l'2 (1e2ei;Ij-roo'{M ,08. 5l;it0' [6'1l' l5] -Math' Kl' Phvs' Math' wiss. ua;i ,ritirt,t Abbirdungen'

g0g. Marx, A. unter.suchunril 15' @' 68] rr"ria 3a l6',1:10',11' 932i33)'40-6't' 10?(i der Ann. dis Konvergenzrodius Bestgbsc'ho,iuns nin, ",ine, r.910. Niatth,,,,. anilytischen Fu;iktion. (Jmtcehrfun;';;;; Potenzreihecler N{R 1e-128'ul '\bgvl' 4s'7--4s8' ond a Arch.M";; "C' C-' Locolly one-to-onemappings Ofttt" H'' 911. Meistt", Duke Math' J' 30(1963)' schlicht";;;;'^ on theorem classical

';i

er2. fi.::,jf':' ;

qu'une fonction suffisantes-pour '::'condrtio'ts

u n i va l e n te so i th o l omo,pn,.i"".r nr u.r ' .Moscou40( 1933) ,3_2| .

n,r.

t*o.t'l;ll$' ins cutptane'Ptoc''Amer' { ''o' tvpi':j?-::atfunctions ztotl)-807'v', 13'41'551 863-s6;.'tfrn MathSoc.10(1959),

FUNCTIONS (PART D BIBLIOCRAPHY OF SCHLICHT

6I

univulence'Mich' Math' J' P ' BoundedJ-fractionsand E' Merkes, 914. 12',55]

[11', vrn zzetD-1373' 395-400' 6(1959), of o continuedfraction' univalenLce p'; Stott' W T'^9-n 915. Merkes,E' [11'12'55] 2iA(2)-20s3' MR pacificI' vutl'' ioiiqool'1361-13;9' theore'ns for S-J'ractions' p'l it"tt' fr,J - Covering E' Ir{erkes, 916. [15'l9' 28',43'55] zzeiz)-964' run L.',73(1960),333-338' Math. functions' hypergeontetric W' J^ S.tarlike P';;;' E' Merkes, 917. [4' 6' 28] -S';ses-a'a-a, 12(19orj' Soc' il";;' 7u1to,z-65' Amer. Proc. of Stott'W' T.-9' products E' p';-noUt"scn'M' MR 918.Merkes, 960_964. p,oc. Amet.r'lu,n.Soc.13(1a62),

starlike fun"rion,. 26-63.14,6, 431 den Normalabbildungsu. nezieh.ungen.zwischen 919. Meschkowski, funktionenii.ri,i,iedirkinformenAboiltlung.Math.Z. -i. MR 13- 734't6ol i s(tg st), rt4 -r24' der Theoricder Ext:.emalprobleme nfuis, .aus 920. N{eschkowski, Ser' A' I' Math' Abbildung'Ann' 1t"a' Sci' Fenicae konJ'ormen ' pp' M R 14- 361'l59l -P h ys.N o ' l 1 7 (1952)12 zusamVerzerrungssatze {" ':ne^hrfuch 921.Meschkowski,H' menhangendeBereich".co*poiitioMaih.ll(1953),44-59.MR 1 5 - 1 1 6[ .9 , 1 5 ,4 8 ,5 8 ] 9 2 2 . M i k i , Y . ' 4 n o t e o n c l o s e - t o - c o20] tnexfuncttons.J.Math.Soc'Japott MR 19-951'[5', 256-268' 8(1956), of a classof mut'tivalency u'iuot'n'y'ili tn' On U' Minami, 923. 33-35' AcaC'Jap' 12(1936)' functio"' P'ot''lmp' nleromorphic

'*',t"l1r1li;tll,t'r. ,*.

of of- coefficients on certainestimations

univalentanalyticfunctiotts'Ann'Polon'Math'7(1?60)'135-140' [9, 17' 25'39i MR 22A(1)-295' for the ondsuffici'ent J' On tne necessary 'conditions 925. Mioduszewski, p 'alLnt in'the usuclanciin the univat'"iL'l be to analvticfu';;;;;^ pofon' Math' 7(1960)' 127-133'MR generolized'-'"n'"'e""' 27 331 22A(l)-295.14,g, 14' 17' 22' 25' ', of multiplyconnected 926. Mitjuu, t. i '' u'ivalent 'onfo'iot-^opping' RSR (1961),158-160' rlomains.DopovidiAkad. Nuut u[rain. MR 234-618' [60] (Ukrainianl-d*'iu"' English'u-matie') conon univalent of sometheorems 927. N{itjuk,l. P' A generalization Akad' Nauk co:l:ect;ddomains'Dopovidi formal mapsof doubty Ukrain.RSR(1961),1115-lila.rut."inian.RussianandEnglish MR 24A-495'160l summaries) 9 2 8 .Mi tj u k,l 'P 'Quelquesappticatfonsdupr incipedelasym'etr i s oti on' (R u ssi a n .Fr enchandRoum un*i*' .,.- ar ies) .Bul.Inst.P ol i tehn.

h-*--

62

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

26- 980'Ill' 12' 241 1 (1 ) 9 6 1 )'N o ' .3- 4;15- 18'M R I a s i(N .S ')7 (1'fil'tiii^etrizsti'on principle{?' :n annulusand P: I, Mitjuk, 929. AtaO' Nauk Uklain' RSR Dopoviai applications' its of some MR and Englishsummaries) (1962),9-lI'-iikrainian' Ru"iun

'fi13:i.t'3ru*,ru de Rouch,' du th,orbme . Uneg,ndratisation 7 n3o. clasnikMet.-Fiz'Astr' Ser'II'

Drustvo. HrvatskoprirJdoslovno MR 14-32'[59] summarv) (1952)'f q-Zj' Gt'bo-Croatian'-French du th\orime de Ia contrattion 931. Mocanu,p.'+:;;;,i.irslisdtion Acad.R' P' Romine'Fil' s desfonctionsun:ivlalentes. dansla classe 303-3t2'MR 2l-1064' l24l Cluj. Stud' e;';' il"t' 8(1957)' n du t h6ori me de contr acti on io gi rZroi.irot 932. Mocan", . f. ;r;']),r" C a n s l o c" l o s s e d e s f o n c t i o " u n ' ' ' o l ' n MR l e s ' 2lA c 1064' a d ' R '16' P'R mine'Fil' 7'ol5' l4g159' 9 (1958) : c l uj . stu d " i ttt'n ru t' des danslo classe derecouvrement th'eorbme un sur T' P' nrr. fi;:;*,1u, f o n c t i o n s u ' ^ i ' o t " ' " ' G a z ' V f u tand ' f i ' ' SRussian e r ' A ( Nsummaries) ' S ' ) 1 0 ( 6 3 )MR (1958)' FrenJ (Roumanian' 4't3-47'7'

utrivatentes' desfoncticns rtestettnritt nro.i?"3"i;ltJlT. surresrayon.Cftl Stucl' Celc' Mat' ll(1960)' Acad. R' P' Romine' Fil' MR Hu"i-u"'"nd French sumrnaries) (Roumanian' 33'7-34L 7 6 - 7 M . [ 6 , 1 1, 1 6 , 4 2 7 univclentes'Studia tiaora^, sur lesfonctions g35. Mocanu, p. i.'i, U n i v . B a b e s - B o l y a i S e r ' f V f u t t t ' - p t t y t ' ( 1 9MR 6 0 )26-216' ' N o ' l ' 9 1241 1-95' summaries) nu"iun unO-f"*tt (Roumania=n' dons la classede fonctions II 936. Mocarr, ;:';.*;-pria^*r"rrtrr*ot Fil' cluj' Stud' cerc' Mat' R";i;; univalentes'Acacl' R' P' MR nuttiu" and French sumnaries) (196C),qg-iOe' (Roumanian'

2ltl;\#; [il'F' rnivatente'Akad' wetensch' sur tesfo-nctions 93?. 221 826-832' Zbl28-401" ll9 ' Amsterdam, Proc' 45(1942)' normalesde fonctions unall'ti' g3g. Montel, p. Legonssur lesry*iit^ 192?'FM 53-303' [59] queset t'uu oipticdtiort.s'Paris' ou multivalentes. sur tesfon.,',ro,, univalentes 939. Montel, P. LiEons Zbl 6-351' [44] Gauthier-Vill;t' Paris' lg33' locale' C' F-' acad' p. Sur l'univalenceor'ta iuttiuaienie lvlontel, 940. 681 t0't1:^11'

' zbt^r;zoiirbiol'57e-581 Sci.Paris divistes'J' p^rloiiiZtliart-diff6rences

I

94r. Montel,p. sur querqu^ tl_t07.u0, |4,491 ott Math.PuresAppl.(9)16(19;;;;,i]i_zzt.'zvi localeiitent univslentes g42. Montet, p.

s'ur

les Joict'ions

j

I

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

I s

tt t

t !

l

I I

a f

I7

63

(3), 54(1937)'39-54' Ann. Sci. 6cole Norm. Sup. multivalentes. FM 63-290.u4' 431 locales' ou demultivalence g43. Montel,p. sr,, irrtiins casd,univalence 'O"O-237 ' I'l1i Mathemati.uCiu:' f 4(1938)'190-195' methodsin the theoryoJfuncM' Top'olog;cul H;;;, M.; Morse, 944. tionsofacomplexvariable'II'Ann'ofMath'(2\46(1945\' IUR 8-21. [59] 625-6('6. funcof meromo;'phic Deformationclasses 945. Morse,M.; Heins,M' Math' Acta to inteiior transforrnritions. fionsond their cxienslons M R 8- 507'[s9] 7 g (rg 4 7 \,5 1- 103. conformal mappings' Simorr Stevin 946. ''-' Mullencler, P' On some MR lo-o7 ' [16',32] 26(1949),136-1'42' coniormal muppings' Simon Stevin 947. Mullender, P' On some ' 30(1954), 44-47'(Dutch)MR l5-787 l32l angentihertkreisformiger Abbitdung 948. Mu'er, M. zi lonpimen z. +j(tqrg)' 628-636'zbl l7-408' [59] Gebiete.rrroitt. in der Theorieder r-.'^7irr-iinigr'extremal Gr^ssen g4g. t"{yrb Ser' A' I' No' "rg, Funktionen'Atn'Acad' Sci' Fenn' meromorphen 461 '. , 284(1960),9 pp'..MR23A-55'U9' konformen schlichten der I'inea)isierung die iO" i'' 950. N'yrberg,P' Abbildung'n'Ant'Acad'Sci'Fennicae'Ser'A'I'lr4ath'-Phys' , p p ' ( 1 9 5 3 ) ' M R1 4 - 8 6 1[ '4 9 ] N o . 1 4 58 l der konin der Theorie Verzerrungssatz p'i''iiii a'n Myrb.rg, 951. A' N' R' 60' AF Finsia Vet' Soc'Forh formeneAiiiauns' Ofvers' 19'68] , 7 (1 9 1 7 -1 812. ) , FM 46- 551'[9' 15' , 9 5 2 . N a b e t a n i , K ' s o m e r e m a r k s o n a t h e o r e m c o n cAcad' e r n i n Jap' gstor-shaped o7 an analyticfunction' llo:'-'t*O' representatiun 10',12',16] 10(1934),Sit-sio. zbl lr-r2o' [3' 6' g 5 3 .N a b e ta n i ,K.Som einequalities- onmodutiofanalyticfunc ti ons . TohokuMath'J'41(1935)'lO9-124'Zbl12-212'U'3'6'10'13' .ng 1 5 ,4 5 , 6 -7 ,64,66,67i of concernl the sections theorems some on Remarks K. 954. Nabetani, FM 41(1936)'329-336' power ,rrir. i, tt' Tohoku Math' J' 62-366.[3' 20] certain'power series'Tohoku 955. Nabetani,K' On multivalencyof Zbl 14-23'Il4l Math. J. 4l(1936),402-405' in ine theory of conformal 956. Nabetani,K. On Study'sti'o"* 406-410'FM Toi'oku Math' J' 41(1935-36)' rcpresentatio'n' 6 2 -3 7 4[], . 6, 10,37] Math' Sem'Rep' No' 5-6 957. Nagu.a,S. ioA"'' polynomials'Kodai ( 1 9 4 9 )5,- 6 .M R 1 1 - 7 1 8u' 7 ' 5 3 1

64

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

II' Kodai Math' Sem' Rep' 1950 958. Nagura,S. Faber'spolynomials' ' 1 r 7 , 5 3 ,5 4 1 ( 1 9 ; o ) ,l 5 - 1 6 ' M R 1 2 - 3 2 7 theorems in the theory of 959. Nagura, S.; Komatu, Y ' Distortion l(1950)' 25-33' MR 12-490' scltlichrfurrtiin'' Nagoya-Math' J' [ 1 5 , 2 4 ,6 8 ] g60.Nakashima,K.Noteonsubordinotion'Mem'Fal'Sci'Eng'Wasedauniv. 16(1952),ll9-122' MR 14-549'Ul Rev. Fac. Sci. g61. Nazim, T. A. uL,r, arn Koebeschenverzerntngssatz. ' R 1 2 - 1 6 '[ 1 9 ] , 1 3 - 1 1 8M U n i v . I s t a n b u (l A ) l 5 ( 1 9 5 0 ) 1 vsleurs moyennesd'une foncrion 962. Neha ri, Z. Jni iroiri6t6' des 208(1939)'1785-1787'Zbl onalytique.C. {' Acad' Sc^' Paris

2r-r42.ls9)

par les fonctions g53. Nehar\, z. sur la d\formation de la frontiire univalentesconvexes.C.R.Acad.Sci.Paris20g(1939)'781_783. M R 1 - 1 1 2 .[ 4 , 1 0 , 1 5 ,6 4 ] Schworzlemmo' Duke Math' J' 964. Nehar\, Z. A generalizctionof 37] l 4 i l g 4 7 ) , 1 0 3 5 - 1 0 4 9M. R 9 - 3 4 0 ' [ l ' l 9 ' born'eesdons g65. Neha,i, z. u* in6gatit6danslo ti'eoriedesfonctions 224(1941)'1093-1095'\IR un onnenu.C' R' Acad' Sci' Paris 8 - 5 0 8 .U 5 , 2 2 , 6 l ) o.l Qnol.t'ric g66. Nehari, z. Tn' 'itipric moclularfunction and o ^closs 69(19'{7)' Nlathof J. by Hurwitz. Amer. functions J'irstconsidered 70-86. MR 8-454. [59] certain Pro7erties of possessing 967. Nehari, Z. On anolyticfunctions (2) 50(1948),120-136'lvIR univalence'Proc' London Math' Soc. 9 - 5 ' 7 6 [. 1 , 1 9 , 2 2 , 4 5 ] 9 6 8 ' N e h a r i , Z . A n a l y t i c f u n c t i o n s p o s s e s s i n g a p o s i t i v e601 realporl.Duke

37 Math.l. rs0q4si,ioll-to+2'MR l0-29C'12'9' '

969.Nehari,Z-Su-run'*'eorimetieM'Montel'C'R'Acad'Sci'Parls 228(1949),1325-1327.MR 10-696' [59] gT0.Nehari,Z.Thertdiusofrtnit'alenceoftnonalyticfunctio:i'\mer' 43l' J. Math 71(1949),845-852'MR 1l-426' ll2' Bull' g7l. Neha ri, z. The ichwarzian rierivariveand schlichtfunctions' M R 1 0 - 6 9 6 '[ 4 ' 9 ' 3 l ] A m e r . M a t h . S o c .5 5 ( 1 9 1 g \ , 5 4 5 - 5 5 1 ' gT2.Nehari,Z.Onboundedonalyticfunctions'Proc'Amer'\lath' S o c 1 ( 1 9 5 C ) - 2 6 8 ' 2 7M5R' l 1 - 5 9 0 ' 1 2 2 ' ? 7 1 atiied €x{rr'tilol g73. Nehari, z. A ciassof rio;itainlunctions and some ptoblems.Transemer'Math'Soc'69(1950)'161-178'MRl2-l5l'

[5e]

gT4.Nehari,Z.Noieonpositiveharmonicfunctions.J.London\latil. S o c .2 5 ( 1 9 5 0 )1, 9 - 2 6 'M R l l - " i 3 5 ' [ 2 ]

.,1

FUNCTIONS (PART I) BIBI-IOGRAPHY OF SCHLICHT

65

g T 5 . N e h a r i , Z , E x t r e m o l p r n h l e m s ' i n trs-to6' h e t h e oMR r y o f12-4e1' b o u n d u1' e d a i12' 'alytic

73(1eii)' functions.ot;;;: Math' -2?,431

(,'nlii,-i:tT:;:;:^:'Jl e76.-ri;i);i:.!,-,."1''{'f ::::':,i';:{:'ff ' Plementatres Buu.Amer.Marh.soc' anetyric^functions. ,,r'f'.8)rndtd ii.,li, ,rr. 60]l MR 13-222'122', 154-366' 57(1951), York' 1952' Manping]-vi.ciu*-Hill, New g7g. Nehart,z. coln-J-o-r,r,ol 396PP.MR l3-b40' [44] Trans' of i'iniatities -in the theory fuctions' i"*' Z' rt, Neha r ' 7' 22' 25' 979. un is- ti5' [9' zs6' - zge ?5( i953) ' rr" tn '!tt' A me r. t*';f; lineordifof second-order of solutions the zeroes on ,,tl' ' MR 689-697 ,rr. Amer' J' Math' 76(1954)' ferential "n'oi'oni'

Proc'Amer'Math'Soc' of univatence' nrt. '" " l{:,liri',21t'o^' criteria [4'311 MR 16-232' 700-704' itrgs4), and'lineardifferentialequaticns. functions 982. Nehar\, Z. Lj;ntivalent vu'iuUle'49-60'Univ' of Michigan ct*prt* u oi Fu;t;' of Lect. r 6 - 1 0 9 3[ '4 ' 3 l ] P r e s sn, n n e ' u o " t g s s 'M n n-iriy:r::, functions' Duke coefficien'ti ttie 7,.'o,t r\, Neha 983. [e' t'7'2s] MR"tl6-e16'

Math.:.zzigsi'li,-zzt-izt'

9 8 4 . N e h a r \ , Z . o n t h e c o e f f i c i eilR n t s18. o f 728' u n i vl4' a l,16' e n t17 f w' ,t19' c . t42) ,i . o n s . P r o c . A m e r . 7) ,291293' 8 (195 so c. Ma th . meromorphic of ' P" On tne coefficients 985. Nehar\, Z'; Netanyahu |5_23'MR ioc. 8(195,7), e*.,.-rurutl. Proc. schlichtfunctions. . 12,6, g, l'l ' 2l ' 25' 36', 471 18-648 9 8 6 . N e h a r i , Z ' ; s c h w a r z ' B ' O : t nsiig;a)'212-217' ' e ' i e f f i c i e n t s oMR f u n 15-786' i v a l e n t[6' Laurent Amer' Math' s"t' series.Proc'

nni.lf; Inthe scrlli,llt.f,tnctions probtem f,r ,]l;(,t;l7o2n)"rt,,,1^t nur. Dept'Math' 39(1954)'

exteriorof theunit circle'rttti"i;;JNo' 251 StanfordrJ' Zbl58-30519' 17' Funktione'die in gegebenen beschrankte Llber R' Nevanlinna, 988. PunktenvotgescltriebeneWel|reatnnehmen.Ann.Acad.Sci.Fenn. 1 3 ( 1 9 1 9N) ", ' f ' F N l. 4 7 - 2 ' 7 1 ' 1 2 ' l 0 ' ? l ' de s 4 ( Jber dii' schlic- htenAbbildungen R' 9 8 9 .N e va n l i n n a' E i n h e i tkreises' FinskuVtttnufup' - Sot' For handl( A) ' 62 ( 1920) ' ll2' 15' 17' 681 - ' "' N o . 7 , ti s-'FM 47.- 324' io^to'^''Abbitduns Sterngebieten' 990.Nevanlinna,R' nber die'

>---

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

SocietetenForhandlingar63(A)' Oeversiktav Finska-Vetenskaps No. 6 (1921).FM 48-403. 16, 17,36, 421 1936' 99i. Nevanlinna,R. EindeutigeAnalytischeFunktionen. Berlin, zbt 14-163. lsgl W. Ed992. Nevanlinna, R. EindeutigeAnalytische Funktionen. J. wards,Ann Arbor, Mich., 1944.MR 6-59' [591 Univ' Press 993. Nevanlinna, R.; et al Analytic Functions. Princeton 1960, 197 PP. Zbl lW-287. l24l of inner 994. Newman, D. J.: Shapiro, H. S. The Taylor coefficients ' functions. Mich. Math. J . 9(1962), 249-255 l59l problem for analytic functions 995. Nishimiya, H. On a coefficient typically.reolinanannulus.KodaiMath.Sem.Rep.9(1957)' 5 9 - 6 6 .M R 2 0 - 1 8 .[ 1 3 , 1 7 ,2 3 ' 5 1 ] the ex996. Nishimiya, H. on the coefficients of functions starlike in terior of a circle.JapanJ. Math. 29(1959),78-82.MR 23A-618. 12, 6 , 9 , 1 7, 2 5 , 3 6 1 Sci. 997. Noshiro, K. on the univalencyof certainpower series.J. Fac. l b | 4 _ 4 0 | .[ 4 , 1 0 ,| 2 , 2 2 , 3 9 '4 3 ] ) ,5 7 _ 1 6. Z H o k k a i d oU n i v . 1 ( 1 9 3 2 1 998. Noshiro, K. on the starshapedmapping by an anolyticfunction. Proc. Imp. Acad. Jap. 8(1932),275-277' Zbl 5-251' [5' 20] Hok999. Noshiro, K. On the theory oJ schtichtfunctions. J. Fac. Sci' kaidoUniv.Jap(1),2(|934_|935)'129-l55.Zb||0_263.[6,1]'49] J' 1000. Noshiro, K. on the univalencyof certain analyticfuncticns' Fac.Sci.HokkaidoUniv.2(1934),89-101'Zbl9-24''12'6'431 Sci. 1001. obrechkoff, N. sur lespolynomes univslents.c. R.. Acad. FM 60-1033'[4, 6, 14'321 Paris 198(1g34),2049-2050. ttal' 1002. obrechkoff, Nr. sri polinomi univalenti. Boll. Un. Mat. l4(1935),245-247.FM 6l-1 154. 132,491 1003. Obrechkoff, N. Sur lespolynomes univalents ou multivalents' ActesCongreslnterbalkanMath.Athenes,(1934),91-94.FM 6 l - l 1 5 4 . 1 4 ,6 , 1 4 ,3 2 i 100.1.Obrechkoff, N. Sur lespolynumes univolentsou m'ultiv1lenls' Bull. Sci. Math. (2) 60, (1935),36-42' FM 62-377' 16' 14' 321 functions- III. J. Nara 1005. ogawa, S. A note on clo,se-to-convex 201 GakygeiUniv. 9(1960),No. 2, 7-23' MR 25-427' 15' 6' l0' Japon Soc. 1006. ogawa, S. on some criteriqfor p-valence.J. Math' . R 2 6 - 6 1 1 .[ 4 , 1 2 , 1 4 , 1 5 ' 6 8 ] 1 3 ( 1 9 6 1 )4, 3 1 - 4 4 1M Univ. 1007. ogawa, s. some criteriafor univalence.J. Nara Gakugei l 0 ( 1 9 6 1 )N, o . I , 7 - 1 2 . M R 2 6 - 1 2 1 0 [' 4 ' 5 l Kodai 1008. oikawa, K. A distortion theorem on schlichtfunctions' Math.Sem.Rep.g(1957),|40.t44.MR19-iol5.[15,24,46,68j

ffi

SCHLICHT FUNCTIONS BIBLIOGRAPHY OF

(PART I)

61

Sci' properties mean muiiivctentfunclions' MR some On .of 169-175' 1009. Ono,l' gun'iLu Daigaku ittt' e' 4(1951)' Rep. Tokvo 33' 431 , ^ - t i in l 3 - 4 5 3 . l g , 1 7, 2 2 , 2 7 " i n tuna t n nrcorono ( t r o t l (cr i r c o l q r e . B o l l . L' S'rie'funzioniunivalenti onoi,i, 1010.

[4] jire40)-' MR3-201' 113-115' Un.Mat'ttiliji

1 0 1 1 ' o n o f r i , L . c o i , , i 4(1942)'21"1-224' o i , o a t t u t e o r i a -MR d e i 7-424' t e T u n[4' z i o19] niunilalerrfi.Bcll. (2) ltal' Mat' zur Un. Theodorsen von desVerfahrens ii'x'on'nrgentz G' z, Math' opit Arch' t012. Gebiete' t
[se] zbt18-3e5' Math.s".' 4'3ii;ii)'-tzr-tz6' mappingof a circleonto o rec-

V ' A' On the conJ'ormal MR 1014.Oserovic, r'tut'i' r:iiqori'No' 1' 111-ll7'

region'Ukrain' tangular 'iouil,till [59] -u'nifortnizotio'n 1920' der Funktiontheorie''Bertin' Lehrbuch F' th'eorem:lhe ,0,r. 1016.Osserman'R' Koebe's "n"fiiti' nt""icae SerieA' I' No' 258 parabolicto"' e"n' ecaa' (195s)' [24] A t-h;r,tltnopnonn onnahernd kreisfor' konforme A'bbildungen 0ber 'q'' l0l?. Ostrc\"ski'

miserGeaieie'JL;''otut"t"niiotit'ie"itt'39(1930)'78-81' ie nts?f : : ht'chi fu ncti on' oeffic c e nt n o ks r ^:::) r0r 8. :X; ?'':' ..so Sci.Rep.TokyoBunrikap"[.X-rtr933);283-28.|'Zb|,7-2|4. Rep' Tokyo of functioLrs"'Sci' multivale-ncy the On S' Ozaki, 1019. gg'-\oz'"ivl 12-24'14',14' 17' 501 2(1934)' A Daig' Bunrika und multivilencyoJ jjme re'markson the univalency s. ozak,, 1020. No' 31-32(1934)' Tokyo eun'iLu Daig' A' functions'Sti'ntp' li 25' 39'-501 ' 41-55'zvt\-z-zl'i4' 9' 14' ' Sci.Rep.Tokyo functions. ^"tii"ol,ent ot theory the orr S. 14] |02|. ozaki, roi-rse' zbl l2-?A"[4',6' BunrikaDaig' A 2(1935)' sci' Rep' II' oi ^irirolent functions' theory *e on s. 1022.Ozaki, MR 14-34'[6' l3' 14' n'iii+i;+s-g?' stt'' Daig' TokvoBunrika

u7l

,ozr il,*l i:';;' ii;ii;il|

in a muttiptv func't'ions of muttivatent Daig' Sect' A

*tO'-i"tt""Bunrika connecteddomain' Sci' r'tl

js' [4'14' 4(rsn),iri-r MR14-35' p'op'iti"

of multivalentfuncT' Yosida' S'; 1024.ozaki, 9n;;k;'; tions'Sci'Rep'TokvoB;;l;p"ieSect'A4(1949)'137-150' 43' ,501 MR 1 3 -4 5 3'1t+ ' tr ' 19'

68

B I B L I O G R A P H YO F S C H L I C H T F U N C T I O N S

propertiesin matrix 1025. Ozaki. S.; Kashiwagi,S'; Tsuboi, T' Some ' sp(tce.Sci. Rep.tot
llo,351

J. Reine und 1038. Peschl,E. Zur Theorieder schlichtenFunktionen. AngewandteMath.lT6(1936),61-94'Zbl16-35'16'17'24'29' 39,541 ttb' 1039. Peschl,E. ]ber die Bilder von S!':rn7ereiclrcnein uilgenieiner

F'UNCTIONS(PART I) BIBLIOGRAPHY OF SCHLICHT

69

bilcttngsatzimRaumemehrererkomolexerVeriinderlichen.Ber. 46)' il2-ll2(1g47)' MR 9-25' [59] Math. -tagung iubingen.(19 svstemeFunktionen' ^9^"'hriinkte 1040.Peschel,E';' ;;t;';:-'t:ii'i 85-22c' l\'iR15'.510j ln], Math.ann. rlciiqs:)' part' J' London reoi with positivc petersen, rur.'on functions G. 1041. '"-"' 49-51'MR 25-66'121 *u,rh. Soc'.35t1961)' Funktionen'Tubsch-lichte p-.iachsymm.eirisclrc tM2. pflaHz,E. ,t;r 42' 491 \l' 10-307'[5' 10' ingen,pi"t'iutio"' tqf+' Zbl l:unktionen'Mat\' schlichte Pfla nz'I-. (JberP-fachVmirye-tlische 1gra3. 491 z. ^o (rg 3 s),' 2- 8;'FM 61- 35C'u5' Comment' Math' kapizitiit' u-nd Extremull(ing'n A' Pfluger, 1gr4{. 621 to-sto 146', Helv.29(19st, 120-131't\4n 1 0 4 5 .P fl u g e r,A .r t,eo,ieder Rieman- n,,hen- [lachen.Ber ltn,1957.M R .

Abbldungkreisrdrmiger rheorie f1;l:%:;1" 1016. 9'lj:,"r"rmen FM 45-671'[31] P;it';; Rend':z(rqi+)' 34r-34" Bereiche.

analytischerFunktionen' beschriinkunrgen 1047.pick, G. Jil, ai' welchedurchvorgegebenepuntiioiswertebewirktwerden.Math. FM 46-4'74'l59l Ann. 7?(1916),'7-23' i"irrrrungssatz' Leipzig Ber' Koebesch.en aen pick, ul'ir G. 104g. 6 8 (1 9 1 6s8), 64'FM 46- 550'u5l l 0 4 g . P i c k , G . i o i r a i e k o n f o r r n i A b b i t d u n gGebiet' e m e s KWien' r e i s e s Ber' aufein b'eschranktes zugleich und schlichtes rv +e-ss3' 122'49ll 2'47-263' 126(1917), Leipzig t'o'to)i"n Abbildung' Ber' 1050.Pick, G' Zur schtichten 3-8' FM 55-789'{60l 81(1929), Ber' Sachs'Ges' Korbeschen'verzerrungssatz. den pick ,c.0i', 1051. 61' 681 Ma th . n o ( t%t) ,6l- 94' u5' .22' 1052.Pinnev.e,.A.onanoteofGalbraithandGreen.Bull.Amer. 10-39 .tt'l Math. sot' :+trq 48)' 527' MR ,Dokl' reelleFunktionenim Kreisring' typisch t)ber E' L' Pir, 1053' zbr's2-8t' (Russian) gztibijl, 6ss-7}2.

AkadNauksssR(N.s.)

im Kreisring. Funktionen ,oro. $i3r,f..,{.,::) Theorieder_schtichten Zbl (Russian) qltr g53)'475-477' Dokl.Akad'NauksssROls'l 5P1r::i"ftt Sem' schtichtfunction' abh' Math' An isotated 1055. U6l zii-ztg'-Mr 22L(D-1629' univ. Hamburg24(1960)' tug.tlorige Extremalprobleme ,rna 1056. pirl, fro,t.rrn."fu*.nr.hur'.;r Z' Martin-I'uther-Univ' HalleWitt' der konformen Abbildung'

** t7-33s'[591 +ii-qssl'1225-1252' witterrueie

70

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

von P. Kcebe. Gesellschaft 1057. Plemelj, J. Uber den Verzerrungssatz 9l 3)' DeutscherNaturforscher und Aertze, Verhandlungen,85(l II, 1, 163.t151 univalence' 1058. Pokornyi, V. V. On some sufficient conditionsfor Dokl.Akad.NaukSSSR(N.S.)79(1951),743_746.MR|3_222. [4,31] of s 1059. Polak, A. I. On s property of tocatly univalentfunctions complex variable. Dokl. Akad. Nauk sssR (N.S.) 96(1954), 241-243. MR 16-25. tsTl Ann' 1060. P6lya, G. tiber anolytischeDeformqtionen einesRechtecks' Math 34(1933),617-620.FM 59-348' t59l Paris 1061. P6lya, G. Sur la syrnmetrisationcirculaire.C. R. Acad' Sci' 230(1950),25-27.MR I 1-435. t59l de I'ex1062.P6lya, G.; Schiffer, M. Sur la reprlsentaticn conJ'orme Paris t€rieur d'une courbe ferm^e convexe. c. R. Acad. Sci' 248(1959),2837-2839.MR 2l-783. 17, 491 Poussin 1063. P6lya, G.; Schoenberg,I. J. Rentarks on cie la vall€e Math' J. Pacific meensand convexconformal maps of the circle. 8(1958),295-334.MR 20-t176. 14,6, 10, 16,471 l' 1064. P6lya, G.; Szeg6,G. Aufgaben und Lehrsatzeousder Anqlysis' II.Do'rerPubl.,NewYork,lg+5'MR7-418'[44] 1C65.P6lya, G.; Szegci,G. IsoperimetricInequolitiesin Mathematical Princeton,l95l . MR l3-27A' t59l Ph1,sl,tt. anci 1066. Pommerenke, Ch. On some problems by Erdds, Herzog' Piranian Mich. Math. J. 6(1959),221-225.MR 22A(l)-125' t59l Mich. 1067. pommerenke, Ch. On the derivative of s polynomial. Math.J.6(1959),373-315.MR22A(l)-16'122'321 of subordinatefunctions. Mich. tc6g. pommerenke, ch. on seauences Math.J.7(1960),181_l85.Zb|9|_252.MR27-316.u] 1069. Pommerenke, Ch. Uber die Mittlewerte und Koeffizienten multivalenterFunktion?tt. )rlath Ann. 145/ t46(1962),285-296' l v I R2 3 A - o 1 1 .[ 3 , 1 4 , l i , 3 3 1 con' 1070. Pommerenke,Ch. Imagesof convexdomains under convex 257-269.t10l formal mappings.Mich. Math. J. 9(1962), schlichter meromorpher 1071. Pomm.r.nk., ch. tlber einige klossen MR 28-258'[1, 3 , 4, 5, Funktionen.Math . 2.78(1962,\,263-284. 6 , 7 , 9 , 1 0 , 1 5 , 1 7, 2 5 , 3 6 , 3 7 , 3 8 , 3 9 , 4 9 , 5 8 ,6 3, & l 1072.pommerenke, ch. on the coefficients of close-to-convexfuncMR 26-980'[1, 3 ,4, 5,6' tions.Mich. Math. J. 9(1962),259-269. 7 , 9 , 1 5 , 1 7 , 2 5 ,3 6 , 3 8 , 4 9 1 J' London 1073. Pommerenke,Ch. On starlike anC convexfuncticns'

f I !

I

t

I r T

i'

t t? i I

t

t

(PART I) BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

1I

Math.Soc.37(|962),209-224.MR25_254.|6,7,10,15,17,18, 22,23,30, 36, 38,631 |0T4.Pommerenke,Ch.onhyperboliccopacityandhyperboliclength. Ir{ich.Math.J.10(1963)'53_63.MR26_t208.[59] functions' ch. on starlike and close-to-convex pommerenke, 1075. Proc.LondonMaih.Soc.(3)13(1963),290_304.MR26_499.|5, 6 , 7 , 8 , 1 7, 3 6 , 3 8 ,5 4 ] starlikefunctions.PacificI. Ch,on meromorphic |076. Pommerenke, I'lath.l3(1963),221-231MR27-59'[6'9'15'17'18'23'25'36' 58,631 propri6t6sdesfonctionsd'une variablecom1077.Popov,B. s. Quelques MR 2C-24(1954)' 4(1953), plexe.Bull.So1.Math.'phis.Macedoine 15-863. t59l

- -) , : ^ t - - , ! n r { n n h

parsilerschtitztheoremunendrich vielfoch 107g.posser, R. de zum Math' Gebiete.Nachr' Ges' wiss' Gottingen' zusammenhangender -Phys.Kl. (1931),199-202'Zbl 3-314' [9' 60] reprlsentation conforme' J' Postel, R. Quelquesprobt\mes ce 10.79. (1932),1-98. Zbl6-263 ' 16',621 Ecolepolytechnique,Cahier30(2), ccnforme propri€t1sde la repr1sentatic'n 1080. possel,R. Sur qurtqurl, rerationavecie th€oramedesfentes desmurtip!emenlccnnexes,^en Zbl 5-363' t60l parcttdtei.tvtattr.Ann. 107(1933),496'504. of coefficientsof odd univalent 1081. Potugina, I. v. on estimation ' Nauk SSSR(N.S.) 85(1952),l2l5-l2l'l frnctions. Dokl. Akad. MR 14-260.u7 , 45, 521 Ft:nktionen'Ark' Mat' 10g2. prawitz, H ioi, Mitteiwerteanalytischer 6, l -|2. FM 53-307, |3,27| Astron. och Fysik 20(1927/28), No. conqui donnentla reprbsentation 1083.Privalov, J . Sur lesfonctions f o r m e b i u n i v o q u e ' R e c ' M a t h ' D ' I ' S o c15', ' M a58] th'D'Mos:ou 9' 10', 31(l g24),350-i65. FM 50-254'[6' of Analytic Functiorzs'2nd 1084. Privalov, I. l. Boundary Properttes 1950' (RusEd. Gos. lz. Tehn. -teor. Lit., Moscow-Leningrad' sian)MR 13-926'[59] constanf'Amer' J' Math' ,H. On tt , nto,h-Landau 1085. Rademacher 65(1g43I 387-393.MR 4-270' ll9l konfomen Abbildungen' 1086. Rado, T. Zur Theorieder mehrdeutigen A c t a S z e g e d : ' ( | 9 2 2 ) , 5 5 _ 6 4 . F M 4 8 _ 1 2 3 5 . [ 5 9 ] variables' de do-maines 1087. Rado, T. sur la repr\sentationconforme ActaSzegedl(1923),180-186'FM49-247't591 lC8S.Rado,T.Bemerkun'genuberdiekonformenAbbildungenkonvexer g2g),+zg-qzg.FM 55_208.u, 10, 37, Gebiete.Math. Ann. 102(1 601

12

FUNCTIONS BTBLIOGRAPHYOF SCHLICHT

propertiesof the derivativeof extremal on I. a. Rahmen, 10g9. potynomiatiandratiionalfunctions.J.LondonMath.Soc. ,334-336'MR 23A-328't59l 3s(1960) functions.Dokl' the theoryoi univarent 1090.Rahmanov,B. N . on Akad.NaukSSSR(N.S.)78(1951),209_211.MR112_8|6.|4,6,

r'el. f;#"i31,

Dokl' B. N. on thetheoryo.funivaten_t-functions. 13_640. [6, 10]

2), 34|-3M . MR Akad. Nauk SSSR(N .S.) 82(195 Dokl' the theory of univsren_t _functions' 1092" Rahmanov, B. N. on A k a d . N a u k S S S R ( N . S . ) 8 8 ( 1 9 5 3 ) , 4 1 3 - 4 | 4 . M R 1 4 _ iDokl' 40.t|zj of univaren_t theory the on . N B. -functio'ns' 1093. Rahmanov, A k a d . N a u k S S S R ( N . S . ) 9 1 ( 1 9 5 3 ) , " 7 2 9 - 7 3 2 . M R i 5 - Dokl' 413.[49] theory'of univalen-t the on N. -fimctions' ts. 1094. Rahmanov, A k a d . N a u k S S S R ( N . S . ) 9 7 ( 1 9 5 4 ) , " g 7 3 _ g 7 6 . M } 1 6 -Dokl' |22.t4,6] theory'o.funivareni-functions' the on N. B. i095. Rahmanov, 369-371'MR 17-249'l4',6', Akad. Nauk sssR tN's') 103(1955);

r0e6 l.t;li;3li?

ands,ied resutts' inequatitv r. caratheodorv's

Math.Stucient9(1941)"13-77MR3-201 ' t 5 9 1 resurts'll' ,nequolityand--auied 1097. Rajagopal,c . T. cara'thecdory's 611 (1948).Vrir to-a+l' tl 5 ' l'7',22',30', Math. Studentl5(1g47),5-'7 Amer' for analytic.functions' 1098. Rajagopal, c. T . on"inequalities Math.Mon.60(1953),693_695.MR15-412 . | | 5 , | 720(1952), ,22,30,5r] on po,|er series.Math.Student 1099. Rajagopal,C .T. A note MR 15-113'12'20'221 gY-rdi(19s3)' clossof power an qbsoluteconstantfor c 1100. Rajagopal, c. T. on 267-270.MR 20-874' l59l series.Math. s.uni. 5(1957), absorutevaruesand fcr coefficients 1101. Rakovic, K. Inequatrities10r ofcertoinregulorfunctiolrs.ActaFac.Nat.Univ.Carol.,Prague MR e-232' UC' 14' 15' l?l 28-31(1946)' No. 172(1939), | | 0 2 . R a o , K . T w o t h e o r e m s o | l b o u n d e d f u n c t i o6ll ns.J.LcndonMath. 19-736't15''22' Soc. 32(1957)'430-435'MR Math' Soc' boundedfunctio"' J' Loncion on theorem A K. Rac, 1103. ' 5 ', 22', 6l l 36(1961),47 4-479' MR 26-615 il l l 0 4 . R a u c h , s . E . M a p p i n g p'pu.iri. r o p e r t i e s o f C e.s a4(1954), r o s u f t l s109-121 o f o r d e'r tMR woof J. tutattt ,riirrl geometric the 15-697.[2C' 35] ,__^^de )^ {,t, mtes.C. R. Acad. univttle clssse fonctions une Sur M' 1105. Reade, Sci.Paris239(1954),|758-1759.MR:16-579.|2,4,5,6,|7,36, 3 8 ,4 l i Math' univaleri functions' M!ch' 1106. Reade,M' On close-to-convex - 2 5' [ 4 , 5, 6 , i 7 , 3 6 , 3 8 , 4 2 1 J . 3 ( 1 9 5 5 )5, 9 - 6 2 'M R r 7

(P A R T I) B IBL1OGR A P H YOF S C H LIC H T FIJN C TION S

13

Duke The coefficients of close-to-convexfunctions' lr4. Reade, 110j. M a t h . J . 2 3 ( 1 9 5 6 ) , 4 5 9 - 4 6 2 . M R | 7 _ | | 9 4 . | 4 , 5 , 6 , 1 0 , 1 7 , 3 6.' 3 8 ] the coefficientsof certain univqrentfunctions 1l0g. Reade, M . on AnnAcad.Sci.Fenn.Ser.A.l.l.io.2|5(\956),6pp.MR 4 0 ' 6 3 ' ,6 - 4 i 1 7 - 1 0 6 9[.4 , 5 , 6 , 1 5 , 1 7 , 3 6 , 3 8 ' Report of unit,alence for \3e-"dt. Prc,hminary I l0g. Reade,M. A riadius B,-rll.Anrer.Math.Soc.Abstract63,lg3(i95?).i28] l l 1 0 . R e a d e , M . o n ( J m e z q w a , s c r i t e r i a f o r u5n 28i ivalence,J.Math.Soc. ' Japan 9(1957),214-238'MR 19-642' [4' il. J. Math Soc. (Jmezawa'sci.iterio for univuience. l r l r. Reade,M. on japan 10(1958),255-259'MR 20-877' l4l functions' Mich' of close-to-convex lll2. Reade,M. Two applications gl-g4' MR 20-404' 14'5' 281 Math. J. 5(1958), J. partiar sumsof certainLaurent expansions. 1113.Reade,M. on the M a t l r . S o c . J a p a n l g ( 1 9 6 3 ) , 6 6 _ 6 8 . M R 2 6 - 4 9 9 . | 9 , 2 0 , 4cer3] of certainfunctions for values of domains The I. M. l l 14. Red,kov, t a i n c l a s s e s o f b o u n d e d u n i v a l e n t f u n c t i o l r s . D o k l . A k -Dokl' ad.Nauk Transl' soviet Math' (Russian) 133(1960),284-287. sssR 484-851.MR 23A'330't291 1(1961), a certsinfunctional in the class lll5. Red,kov, M. I. The range o-f S,(d(w)).Izv.Vyss'Uc'laved'Mat'1962'No'2(27)'ll9-129' (Russian)MR 25-796' 122'621 certainfunctionarin the crasss'' 1116.Red,kov, M. I. The raige of a 134_142.(Russian) Izv. Vyss. Uc . Zaved.tutut. |g52, No.4(29), MR 25-796.t22, 621 anarytic functions. l1 1?. Reich, E. An inequarity -for subordinate 15-862. [1, 3' 18] pacific J. Math. 4(1954) , Zig-214.MR theoremof Beckenbach'Proc' I I lg. Reich, E. An alternateproo1 o.f a 37] , 578-579.N,IR|6-24. [3' Amer. Math. Soc. 5(1954) Math' Soc' Amer' Proc' 1119.Reich,E. on a Bloch-Landauconstant' ? ( 1 9 5 6 ) , 7 s - 7 6M. R 1 7 - 1 0 6 6t' 1 9 l coefficients.Duke Math' J' 1120. Reich, E. Schtichtfunctions with real . Zbl 70-299' tl3' i5' 22' 23' 24' 391 z3(lqio), 421-427 Acad' Sci' Fenn' Ser' A' 1121.Reich,E. on radial slitmappings.Ann' 12 pp' MR 23A-618'[59] I. No'- 296(1961), ccnforntalmaps o"f llZZ. Reich, E.; Warr.r,u*oi i, S. E. On canonicsl J' Math' 10(1960)' regions of arbitrary connectivit\' Pacific 965-985.MR 22A(2)-1376'122'241 Abbitdungen desEinheit1123.Reinhardt, K . (Jberschlichtekonforme 83-86' FM 54-378' skreises.Jber.Deutsch.ver. Math ' 37(1928)'

uel konformer Ab1124.Remak, R. ueber eine spezielleKlasseschlichter

14

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

B t1' 175-192; L2' bildungen desEinheitskreises.Mathematica MR 8-22. 14,6,32, 621 43-49(1943). in the crassof typically-real p rrz5. Remizova,M. . Extremarprobrems functions.Izv.Vyss.IJc.Zaved.Mat.(1963),No.1(32),|35_|M. MR 26- g82. [9, 13, 15, 23, 29, 58, 66] der konformen Abbildung' 1126.Rengel, E. Einige schtitztheoreme 1(1933)'139-162'FM schr. Math. sem. Inst. Math. univ. Berlin 5 9 - 3 5 1 .[ 5 e-Existenzbeweise ] mehrfach fur schlichte Abbitdungen llzj. Rengel, b. Nor malbereiche'Jber' Bereicheauf gewr'sse zusammenhiingender 60_286.[60] Deutsch.Ir{ath.-Ver. 44(|934),51_55.FM bei schtichterkonformer Ab1128. Rengel, E. Verzerrungi^ Rindes MR 5_37.[9' Math. 6(1942),370-393. bildunge|l,I,II. Deutsctre

lel of schticht functions.Publ.Math. rrzg.R6nyi,A. on thecoefficients ta-i:' MR' ll-92' U0' 17'38' 41'421 1(1949;, Debrecen

mapping' Acta Sci' 1130. R6nyi, A. Ort the geometry of confo:"mal Math.Szegedl2B(1950),215-222'MR11-(49'17'491 II' Ann' Acad' 1131. R6nyi, A. Son e remori, on univalentfunctions p p ' t v I R2 2 A ( l ) " 1 2 8 [' 5 ' s c i . F e n n .S e r .A . I . N o . 2 5 0 / 2 9( 1 9 5 8 ) , 7 1 2 , 1 5 , l b , 1 7 , 3 8 ,6 4 1 Bulgar' Akad' ll Jz. R.6nyi,A. Som, ,r^irks on univalentfunctions' B u l g a r i a nR ' ussian N a u k I z v . M a t . I n s t . 3 ,N o . z , 1 1 i - l 2 1 ( 1 9 5 9 ) ' summaries)MR 22A(l)-128' [5' 17' 38] per refunzioni maggioanti ,33. Ricci, G. su un probii^o di mqssimo Nincei' Rend' cl' Sci' Fis' delleseriedi potenze. Atti. Accad. Naz' Mat. Nat. tsi r8(1955),609-613.MR l7-1070. t39l einer stetigenFunktion l134. Riesz, F. Uber die Fo,urierkoeffiz'ienten 2(1918)' 312-315'FM von beschrankterschwankung.Math ' z'

46-4s2.

t5el Interpcrstior;sformelund einige 1r35. Riesz,M. Eine trigonometrische Ver' (Jngteichungen-fur Poiynome. Jber' Deutsch' Math' FM 45-405' [59] 23(lgr5),354-368. ' Math ' z' 27(1928)' 1136. Riesz, M. sur les fonctions conjug€es . 218-2M. t59l , a 1^ c. Sct' Acta holomorphes' 1137.Riesz, M. Remarquesur lesfonclions Math.Szeg,-dl2A(1950),53-56'Zbl38-229't591 Krummung ebenerKurven bei I 138. Ringleb, F. (iber das Verhaltender konformerAbbildung.Jber.D.M.V.45(1935),57-60.FM s l - 1 1 5 6 [. 3 5 1 Royal M. S' '4 noteon schlichtpolynomials' Trans' 1139.Robertson, 431 , Soc.Canada(3) 26(1932),43-48. Zbl 6-147 132,

FK BIBLIOGRAPHYoFSCHLTCHTFUNCTIONS(PARTI)75

functions' thecoefficientsof a typically-real I140. Robertson,lvl. S. On 1 2 - 2 1 2 ' 1 21 '3 '1 ? ' B u l l .A m e r .M a t h .s o c .4 l ( 1 9 3 5 )5, 6 5 - 5 7 2Z. b l 2 ' 3 ,4 5 ,5 1 ,5 2 1 fuitctions.Bull. M.s.,4 remarkon the odd schricht r141.Robertsotr, A m e r .M a t h .S o c. 4 2 ( 1 9 3 63) ,6 6 - 3 7 0F.M 6 2 - 3 7 3t 'l 6 , L i , 2 4 ' 4 2 ' 45, 521 ' starlikein one direction 1142.Robertson,M. S. Anatyticfunctions 1 0 ,1 3 ' 1 7' A m e r .J . M a t h .5 8 ( 1 9 3,64i6 5 - 4 7 2Z. b l 1 4 - 1 2 0 . 1 2 , 6 , 23, 36,38,40, 41, 421 oJ-aunivaient of the coefficients 1143.Robertson,M. S. On the o;'der 937),205-210'zbl 16-126'13'7', function Amer. J. Math. 59(1 1 5 ,l 7 , 4 2 , 5 4 .6 2 ,6 8 1 of univalentfunctions.Ann' ll*. Robertson,M. S. On the theory 1 0 'l 3 ' 1 5 'l 6 ' M a t h . 3 7 ( t 9 3 6 ) , 3 7 4 - 4Z0b8l 1' 4 - 1 6 5t l' ' 2 ' 3 ' 4 ' 6 ' ? ,0 , 3 6 ,3 8 ,4 1 ,5 1 , 5 4 ' 5 6 ; 6 1 6' 3' 6 4 '6, 6 '6 8 1 17,20,21,22,23 of Ceshrosumsof univalent 1145.Robertson,M. S. on the univalency 241-243'FM 62-36i' Bull. Amer.Math. Soc.42(1936), lunctions. 14,20, 3Zl o.fa univalert coefficients 1146.Robertson,M . s. on the ordero.fthe s9(1936).205-210'zbl 16-1'26'13'7' function Amer. J. Math. ' 8] 1 5 .1 7, 4 2 ,5 4 , 6 2 6 of all analyticfunctiortsin 1147.Robertson,M. S. A representation 38(1937)' termsof functionswith positiverealparf' Ann' Math' 770-783.2b117-407.12,13,15,17,21,23'28'36',40',45',51',52', 5 6 ,6 3 , 6 6 , 6 7 1 p' Bull' Amer' 1i48. Robertson,Ivt. s. Multivalentfunctionsof order Zb\ 18-315'U4' 171 282-285' Math.Soc.44(',938), infinitelymany 1149.Robertson,M. S. On certatnpowerserieshaving 339-352'Zbl2l-143' [13' Ann. Math. 40(1939), zerocoefficienls. 1 5 ,1 7 , 3 9 , 4 5 , 5 16, 6 1 univalency of analytic functions ' 1150.Robertson,M. S. Piecemeol 50, 54, l2O-128'zbl 20-i 41. [3, 14, 15, Ann. Math.40(1939), "7, 5 7 , 6 5 ,6 8 1 an analYtic V 1151.Robertson,M. S. The variationof the sign of for MR r-9. 12,3, sr2-519. 5(1939), function U + iZ. Duke Math' J' 1 4 , I 5 , 1 ' , 72 1 , 4 9 , 5 0 , 6 5 ] : 0 for n - 0 1152. Robertson,M . 5. Typicaity-realfunctions with Qn 1-214' (mod 4). Bult. Amer. tvtaitr.Soc. 46(1940),136-141'MR

u3,17,39,51,521

starlikefuncI153. Robertson,M. S. Thepartialsumsof multivalently g29-838. MR 3-79.16,14,20,431 tions.Ann. Marh tzl izog4t), functions' 1154.Robertson,M. S. Starcenterpoints of multivalent

16

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

DukeMath.J.l2(1945),669-684.MR7_379.|2,6,14,15,|7,19, 2 1 , 3 6 , 5 05, 4 ,5 6 ,6 3 ,6 5 ,6 8 1 of univaleryfynctions' Bull' 1155.Robertson,M. s. Th* coefficients M R 7 - 1 5 0 u. 3 , 1 7 , 3 9 , 4 5 , A m e r .M a t h .S o c .s r t r g +s \ , l l l - 7 3 8 . 541 . ..!tl^*.,tt withmultiplymonotonrc powerseries M. s. univarent ,56. Robertson, Sequencesofcoefficienfs.Ann.Math.(2)46(1945),533-555.MR 7 -201. 14,6, 13, 20,23, 39' 411 o1.alemmaof Feier to tvpicallv1157.Robertscn,M. S, eiiiiroiioni realfunctions.Froc.Amer.Math.Soc.l(1950),555-56i'MR 12-248.tl3 , 39, 41, 471 problemfor functionsregularin 1158.Robertson,M. s. A coefficient g52),407-423' MR 14-460'[13' an snnulus.Canad.J. vtatt,.4(1 1 4 ,1 7, 4 9 ,5 0 ,5 1 1 starrikefunctions.DtrkeMath. J' M. s. Muttivarentty r 159.Robertson, 2 0 ( 1 9 5 3 ) , 5 3 9 - 5 4 9 ' M R 1 5 - 6 1 3 ' l 6 ' , 1 3 '+, 1pw 4 ' ,-1 60'' , 1Trans' J',36',39',50',51] solutionsof w" 1160.Robertson,M. s. schiicht M R 1 5 - 7 8 61. 4 , 6 ,1 0 ,1 3 ' A m e r .M a t h .S o c. l i t t g s + ) , 2 5 4 - 2 7 4 . 3 1 ,4 i l Dirichtet series.canad. J. Math' il6r. Roberrscn,M. s. schticht MR 20-664't281 161-176. 10(1958) partialsumsof harmonicseriesexpan1162.Robertson,M. s. cesfiro MR 2l-413' 14,13' ?',g', sions.pacificl. vraitr.8(i958),829-846. 23, 4ll to of the subordinction PrinciPlc M' S' Applications 1163.Robertson, 11(1961),315-324' MR u'nivslentfunctions' Pacific J' Math. 23A-329.U, 6, 101 of schlichtfunctions' Proc' ll*. Robertson,M. s. convolutions A m e r . M a t h . S o c . r l ( r g o z ) , 5 8 5 - 5 8 9 . M R 2 5 _with 2 5 4positive .|6,9,47| J'orfunctiuns M. s. variationalmethorts I165. Rober*,son, soc 102(1962),s2-93' MR rear part. Trans. nmer. Iviath. 24A-612.ll , 23, 241 problemsfor analyticfuncions with I166. Robertsor,M. s. Extremal Trais. Amer' l'{ath' Soc' positiverea! pari qnd appiicotiotts. , l 4 ' 6 ' , 9 ' ,1 0 ' , 1 2 'N 1 0 6 ( 1 9)6, 2 3 3 6 - 2 5 3M ' R ' 2 6 ' 6 5 '1 2 ' , of convexityP'oblems'Mich' 1167.Robertson,M. S. Someradius

} v i a t h . J . l 0 ( i 9 6 3 ) , 2 3 i - 2 1 6 . I . { R 2 7 _ 3 |a3 schticht . i 2 , 5 , 9furiction' ,12,161 u for constqnt Btoch The M. R. '6g. Robinson, Zbl'|2_171.u9] Bull. Amer.lr'{ath.Soc.4l(1935),535-540. ,,on ihe theoryof Chen,spaper: -+r(i935), 1169.Robinson,R. NI.A note on 327428' zbl i. schtichtfunctions." Tohoku Math. 14-70.u6l

BIBLICGRAPHYoFSCHLICHTFUNCTICNS(PARTI)1-t

1 L',l 7 0 . R c l ; i n s o n , R . M . B l o c h f u n c t i o n s . D u k e M a t h . J . 2 ( | 9 ? 5 ) , . zbl 15-30'U9l 453-459 M. On tie mean valuesof an analyticfunction' ll.ll. Robi:rson,R. 489-u51.MR 2-79' t3'! Bull Amer. Ir{ath.Soc. 46(1940), ||T2.Robinson,R.M.BouLndedunivolentfunctions.Trans.Amer. M a t h - S o c ' 5 2 ( 1 g 4 2 ) ' 4 2 6 - 4 4 9 ' M R 4 - 7 7univ' ' t l 5 ' 2calif' 2 ' 2 4Publ' '61'oEl analytic functiirt. Bounded . M R. 1173.Robinson, 5-259'U5' 221 Math. (N.S.)l(1944)'13l-146'.MR Trans'Amer' Matir' Soc' Unlvalcntmajttrants' 1174.Robinron,i. fuf. 6 1 ( lg 4 7 ) , 1 - 3 5M. R 8 - 3 7 0 '[ l ] ||7).Robinson'R.M.Extremalprobte m s16-1096. forstarm p p 68i ings.Proc. [6,a15, MR Amer. Math. Scc.o(iqls), loq-lll. q of map' conditions for univalence lli6. Rogozin,V. S. Twotrnii''nt ping.Rostov.Gos.univ.Uc.Zap.Fiz.Mat.Fak.32(1955),135137. MR I 7-724'.!4, 9' 281 bei potenzreihenund ihren Bitischranken uber w. Rogosinski, rrjj. Abschnitten.Math.Z.|7(|923),260-27(,.FM49-23|.|2,|3,20, tJlr"rinski, sinusentwickrungen. w. tiber positiveharmonische 1l7g. r)' 2' Abt' 33-35't2l Jber.Di;;h' Math' ver' 40(193 Funk(Jberden wertevorrateineranarytiscrrcn rr.7g.Rogosinski,w. tion.Schrift.Konigsberg,Gel.Ges.,Naturw.Klassc,S(1931)' i-31 . zbl 2-272'[.1'9' 19' 37ll und Entwicklungen poiiti" harmonische 1180.Rogosinski,W. tlUelr' typischreelePotenzrernen.Math.Zeit.35(1932),93-|2|.Zb| 3-393.12, 13,231 r ^ - Funktiontheoric D,,-rrtinttthpnr' ' d:! I 181. Rogosir:ski,w . zum Maiorantenprinzip Math.Z.37(1933)'210-236'Zbl7-167'U'2 1 Lernma' Jber' Deutsch' I182. Rogosinsl:i,w. zum Schwarzschen Math.Ver'44(1g34'S'25t-261'Zb"f0-307'122'371 meinerArbeit: zum schwaruchen 1183.Rogosinski,w. Nachtragzu L e m m a . J b e r . D , . M . v . + s ( r 9 3 5 ) , 4 8 , 2anaiytischer 4 3 . F M . 6 1Funktion -348.[371 w . uber den wertevorroieiner l rg4. Rogosinski, sind' CompositioMath' 3(1936)' von der zwei Wertevorgegeben 199-226.Zbl14-353' [9' 19' 221 Phil' functions'Proc' camb' w. on subordinaie 1185.Rogosinski, l-26' Zbl20-140'Ul Soc.35(1939), J' LonnpU'rbach-Eilenberg' 1186.Rogosinski,W. On a theoremof donMath.Soc.14(1939),4_||.Zbi.20-376.(1,3,16,|7,|9,22, 341 of subordinatefunctions' I 187. Rogosinski,w . on the coefficients proc.LondonMath.Soc.(2)48(1943),-48-82'MR5-36'll'2'3'

b--*-

7E

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

6 , 1 0 ,1 7 ,1 9 , 2 7, 3 9 , 4 2 1 W'; ShaPiro'H. S. On certain extremum Problems 1188.Rogosinski, MR Acta Math.90(1953),287-313' for analYticfunctions' 1 5 - 5 1 6[ .5 9 ] du cerclede conA. sur ls repr€sentqtion-conforme 1189.Rosenblatt, Krak' Bull' (1917)'575-585' d''unes6riede'puissonces' vergence 68] FM 46-554.[9, I 5, 17,18, lg, 54'58', dansle cer' univslentes de puissances A. Sur les's€ries I190. Rosenblatt, cleunit€.Cir.Acaci.Sci.Pariszcz(t938),442-444.zbl|9-272. ll7 , 45, 52, 541 born\edansrecercreunit€.Bu[. soc. A. sur ress€ries Rosenblatt, 11g1. FM 6l-346' t15' 20' 22' 6ll Sc.Liegeitrqlsl ,..124-127' schlichtenFunktionen im rr9z. Roserrblatt,A. uber die reguraren 165-176.(Spanish)zbl Rev. ci. Lima 40(1938), Einheitskreis. 20-141.t17, 27, 45, 52, 541 der schlichtenReihen im 1193.Rosenblatt,A' Uberdie Koeffizienten -179.zbl 20-141. [17' Rev' Ci' Lima 40(1938)'t77 Einheitskreis' 27, 45, 52, 541 vorstehendenNote' Rev' ci' Lima 1194. Rosenbiatt,A. Bemerkungzur 11t,27, 45' 52' 54] 40(1938),1g1 182.(Sparr[n)zbl 20-141. Noten uber die schtichtenFunk1195. Rosenblatt,A. zusatz zu mcinen Z b l 2 0 _ 1 4 1u. 7 , 2 7 , 4 5 , t i o n e n .R e v .C i . L i m u + o ( t 9 3 8 ) 1, 8 3 - 1 8 4 . 52,541 n ,|^--^-.-; donsre desfonctions ,u.nivalente coefficients les Sur A. I 196. Rosenblatt, ' Zbl 2l-143' U 7 ' 541 5-41-545 cercleunit6.Rev. ci. Lima 40(1938), sur tescoefficientsdes s€ries rrg7. Rosenbratt,A. Nouveilesrecherches 547-553-Zbl 2l-143' U7' univalenfes.Rev. Ci. Lima 40(1938),

5+l ner cerchio A. suue funzioni univarentidispari lM-146' l rgg. Rosenblatt, vls 28(1938)' Rend' rtnitario. Atti. Accad. Nur. Lincei

zbl 20-l4l. u7, 27, 45, 52' 541

dansle desslriesunivarentes 11gg.Rosenblatt,A. sur iescoefficients -128' Z'bl 19(1939)'127 cercleunit6. Bull. Soc. N'iath' Grece' 2l' 143.U7, 541 ' Actas of univalentseries 12c0.Rosenblatt,A. On the coefficients - 7 ' l l 7 , 3 9 ' 4 5 ' 5 2 ' 5 4 1 4 A c a d .c i . L i r n a4 ( i g 4 t ) ,1 4 5 - 1 5 5M. R irt theunit circle-Revistaci' Lima A. on pow'erseries 120r. Rosenbratt, ' 22' 301 45(1943t , Ps-zzs' (spanish)MR 5.-176'tl7 anaryticin the unit of functions 1202.Rosenblatt,A. on the mod'urusgqi),27-M. MR 8-19' (spanish) Acad.ci. Linna8(1 circie.Actas

t5el

-_

BIBLIOGR'APHYoFSCHLICHTFUNCTTONS(PARTI)

s€riesde Turski, s. Sur les coefficientsdes A.; Rosenblatt, na3. dansle cercleunit€'c' R' Acad' Sci'Paris univalentes puissances Zbl ll-261' U7', 541 1270-1272' 200(1935), p. c. sonte propertiesof absoluteiyrnonotonrc 1204.Rosenblooirl, 458-462'MR 8-65' Mattr.soc. 52(1946), functions.Bull. Amer. t5el schricht funcH . L. Thecoefficientprobremfor bounded Royde', . 205 r g4g), MR 657-662' 35(1 tions.proc. Nat. Ac;. Sci. u.s.A. ll-426.122,24,291 on q rigitiity of cernin subtiomains corlforn:ql he T L. H. Royclen, 1206. Soc.76(|954),L4-25.MR Riemannsurface.trans. Amer. Math. I 5-51e.[5ei probremfor schrichtfunctions. 1207.Royden,H . L. The interporation MR 16-232.124'291 Ann. of Math. (2) 60(1qi+l, 326-344. rteformation'Reprintfrorn: Lectures 1208.Royden,H. L. Confirmal Univ' of MichiganPress' on Functionsof a complex variable; . i24l 1955.MR 16-1096 of onalyticfunctions' ond starrikeness Conrritty c. 1209.Roysrer,w . D u k e M a t h . J . i g ( I g 5 2 ) , 4 4 7 - 4 5 7 . M R 1 4p-vole;t -261l.[6'10] ' functions omiltedfi't 121C.Rol,ster,w. c. Noteon values D u k e M a t l r . j . 2 2 ( | 9 5 5 ) , 1 5 3 _ 1 5 6 . M R 1 6 _ 6Amer' 8 5 . u 4 ,Math' 16,19,22] univalent functions' Rational c. w. lzlL Royster, MR 17-1069.t39l , 326-_"28. Monthiy63(1956) prob.lgmfor functions regularin an l2|2. Royster,w. C. coellicient MR 2l-1064'[6, l3' 17' elipse.DukeMath. i'.zeggjq), 361-371. 40, 41,571 posit;verealpart in an ellipse' 1213.Royster,W. C. Functionshaving MR'2|-783.|2, |7 ,57ll Proc.Amer.Math.soc.10(1959)_,266_269. |2|4.Royster,w.C.Extremqtproblemsforfunctioryl...............tarlikeintheexMR l4(l962),540-551' teriorof the unit circle.Canad.J. Math. 26-499.[6, g, 16,l7 ,24,251 murtivarentfunctions. rzrs. Royster,w. c. Meromorphicstarrike MR 25-|2||. [6,9, 300_308. Trans.Amer.Math.Soc.roz(1963), 1 4 ,1 7 , 2 5 ,3 6 ,5 0 1 Akad' 1216.Saginyan,A. L. on the theory of univalentfunctions' NaukArmyan,SSR,Izv.Fiz'-Uat'Estest'Tehn'Nauk;9(1956)' N o . 7 , 2 9 _ 3 5 . ( R u s s i a n . A r m e n i a n S u m m a r y ) MJ' R18_728.u9'491 one direction' Math' l2l'7. Sakaguchi,K. On functions star tike in S o c . J a p a n 1 0 ( 1 9 5 8 ) , 2 6 0 _ 2 7 1 . M R 2 0 - 7 7 J' 1 . tMath' 6 , 1 0 ,Soc' 11,12,20,,40] K. On's certainunivalentmapping' 1218.Sakaguchi, ' 14'5' 6l , 72-7s' MR 2r-1063 rapai I 1(i959)

b--

I EO

BIB L IO GR AP H YOF S C H L ICH T FU N C TION S

of murtivarentfunctions. Sci' Rep' rzrg. Sakaguchi,K. some crasses 205-222'MR 22A(l)-18' Tokyo Kyoiku Daigaku.Sec.A 6(1959), 49ll 17 16g , , 1 0 ,1 1 , 1 2 , 1 4 ,1 5 , , 2 0 ' J' Math' Soc' Japan 1220.Sakaguchi,K . A note on p-valentfunctions' 1'+] t4(1962), 312-321' MR 2r-1209' [4' analytic of functions' J' Math' Soc' lZZL Sakai,E'. On the multivalency ' MR 12-601'[6' 14' 22' 43] Japan2(1950),105-113 of the convex functions' Bull' 1222. Sakashita,H. Some subclasses KyotoGakugeiUniv.SerBl4(i959),4-7.MR21-1350.|4,10, 1 5 , 1 7 ,3 8 1 caefficierrfs.Duke ivlath. J. |223. Salem,R. Power serieswith integral r2(1g45),153-172.MR 6-206' t59l Fourier anolysis'D' c' Heath 1224.Salem,R. ,4lgebraicnumbersand and Co., Boston1963,66 PP' t39l of varueof a schrichtfunction' rzz5. SarinaS,B. R. No/e on the region MR 14-460'u5' RevistaMat. His. -Amer. (4)I2Qg52),223-228. 24,29,681 on the Theory of Functions of 1226.Sansone, G.; Gerretsen,J . Lectures Functions' P' Noordhoff a complex variable I: Holomorphic (1960),488 PP' Zbl 93-268' t59l mapping' Math' Notae ', L. A. A theorem on conformal 1227.Santalo, ' 5(1945) 29-40' (Spanish)MR 6-261 t35l congrasdesMathemarzzg. Sario,L. on univarentfu'nctions.Treizieine 202-208' T..'u i Helsinki 18-23Aofft (1957)' ticiensScandinaves, 209pp' MR 2l-783' [9' 60] MercatolsJryckeri, Helsinki' 1958' convexity of bounded functicns ' 1229. Sasaki, Y. Theoremson the P r o c . J a p a n A c a d , 2 T ( | 9 5 1 ) , | 2 2 _ ! 2 9 . M R : 1 3 - 7 3the 3.u 0 , | cir2,22| un:t of the regionsto which 1230.Sasaki,Y. Cn the Hatiptsehne Proc' Japan Acad' cle ,s mappei by th; bounded func-tion' 216-2t8. MR l3-&2' l7' 221 27(1951), 't*3L Sasaki Y . On somefcrnily of multtvaientfimctions' Kodai Math' , 14-649'i4', 6', l0' 14' 351 Sem. Rep. lgsz(lgsz), a4-g} MR boundary valueproblem' contrib' 1232.Schaeffef,A . c. An'extremal (195i)' PP' 4l-47 ' Annais of to Theory of Riemann Surfaces ' Press'Princetotr'N' J ' Math. StudiesNu. 30. Princetonuniv MR 15-24. t62j C' Tht: coo-fficientsof schliclit Junc1233.Schaeifer,A. C'; SPcncer'D' M R 5 - 1 7 5 .[ 9 , 1 7 , 2 4 , tions.I. Duke Math ' J ' 10(1943)' 6 1 1 - 6 3 5 . 25,45,52,541 The coefficientsof schiichtfunc' 1234.Schaeffer,A. C'; SPencer'D. C. 'r-206' ' 22' IVIF il7 tions. II. Duke Math' J' 12(1945),107-i25. 24, 42, 541

I I

I

BIBLIOGRAPHYoFSCHLICHTFUNCTIONS(PARTI)Er

of schlichtfuncA. c.; Spencer,D . c' Thecoefficients schaeffer, 71235. u's'A' i)ogqel' 111-ll6'MR sci' Aca'd' Nat. Proc. tions.III.

inconfor rrtetho'i A vqi'iationa! c. . D tz36iifl;lif;riti. 9., lp:nccr,

m a l m a p p i n g . D u k e N i a t l , . j . l 4 ( 1generol g 4 C , )ctas-s , 9 4 9of_ 9 56.MR9 _34|.i24j in, problems C';.3pencer'D ' C' A A' Schaeffer, 123'7. conformalmapping.p,o..Nat.Acad.Sci.Ii.S.A.3S(|947)' MR 8-575' l24l 185-189. of schlicht funcspenc.i,o. C - Thecoefficients c.; A. Schaeifer, 123g. tions.IV.Proc.}{at.Acad.SciU.s.e.35(1949),|43-150.MR the third Spencer,D. c. Modetsittustrsting c., i*,''n. ltr3? tzSs coefficientregionforschtichtfunctions,scripta.Math.l6(1950)' 'ons 67-71.MR 12-89't291 rcgr for schticht L'oefficient C' ' D 1240.Schaeffet,A' C'; Spencer' f u n c t i o n , . A - . , . M " t h . S o cD..CC. o l lCoefficient . p " u . 3 5 ( 1regions 9 5 0 ) . for M Rschlicht |2_326|441 A. c.; sp.ncer, Mass' |24|. Schaeffer, of i;tt' Cong' of Math" Cambridge' Proc' Trnrtion'" 2(1950),224-232'MR 13-546'l44l method'fcrsimply D ' C'; variational A' C'; Spencer' Schaeiler, 1242. connecteddomains.Proc.ofaSymp.lsg-191.}Iat.Bur.ofStandards,Appl.Math.-Ser.No.18,U.S.Govt.Printingoffice' l24l Wash.,p"C' (1952)'MR 14-'743-' scnirrer,M. The coefficient D.^C.,. ' |243. Schaeffer,A. C.; sp.n..,, '' 493-527 Duke Math' J' 16(1949) regionsof schticn,iuir,ions. M R 1 1 - 9 .11 2 4 1 desfoncpour l'evaluation nouueott principe un sur M. Schifrer, lz*. ' 231-240' bull. Soc. Math' France64(1936) tions holomorplrer. ' , 1 5 ,1 7 1 z b l 1 5- 3 5 9 u de' fonctions podr une{yt^'.tilte '109-7ll' zbl 1245.schiffer, M. un calcuide ,ariation plit 205(1937)' univalentes.c. n. acao. Sci.

*Tyy 1'^Y-:3:u::,',"J""' 3;i']' probti me!' e'xt |246[tffi; :2r1i' conforme.Bull.de.laSocietetvtatt,.-atiquedeFrance,66(1938)' 48-55- zbl18-409'[9' l7 ' 24' 25ll famiry of simple within tr';e variation of metnoa A . M 1247.Schiffer, functions'Proc'LondonMath'S;t'Q)M(1938)'432-449'Zbl lg-222. 124,42, 531 Proc' Lonof simple.functions' 1248.Schiffer,M. on the coefficients d o n M a t h . S o c . ( 2 ) 4 4 ( 1 9 3 8 ) , 4 s 0connec'ted - + 5 2 . a b domains' i t | 9 _ 2 2 2Duke .|24,42,531 multipty of spon The ' M l24g' Schiffer, 4-271' [9' 171 Math. J. 10(1g43),)og-zie'MR

hF-,---

I 82

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

|25o.Schiffer,M.VariationoftheGreenfunctionTydtheoryofthe p-valued'functions.emer.r.Math.65(1943),341-360.MPt 541 4-215.t9, i4, 17,24.' 42' 53', de M' Lowner' c' R' ,6q*1,"r'itff\rrntielle sur M. Schiff.i, rz5r. ' MR 7 -sr5' t24l Acad. Sci. Parrs Zlrtiqas;' xg--lt 1 double-connected ' domuins io'durus of th; on M. fer, schif rz5z. tgt-1r3'MR 8-325'[5e] Quart.i. or Math' titts+i)' snd variation of domainformula nadam)'d''' M' Schiffer, 1253. the in2 5 f u n c i i o n s . A n r e r . l . r v r a t t r . eo!g torthonormar r946),4|7-M 8.MR8.3 .v,9,24| functions 1254.Schiffer,M. An oiiirotii 147-156' Amer. J. Math' 70(1948)' theory0f confornal'iapping.

$lti;?:t*"';i)r 1255.

functhetheorvof univatent potvnomiats-in 10-26'

503-517'MR 54(1948), tions.Bull.Amer.tvtaitr.Soc.

rzs6.ih,?f'il:ti

[9'

mapof conformat in thetheory methods ariatiorrut

p i n g . p i o c . I n t . c " ' ' . n ' a t h . 1 9 5 0 V _ 2 . M RBull' ] 1 1 3Amer' _ 5 4 7 Math' .1241 domain lr,nrtionars. of variatiin . M rzsi. Schiffer, q:+)' 303-328'MR 16-233'1241 Soc.OO(f in the thr>thecrv thecryo1 " in variatioiatmethods of Appric-ations . M 125g.Schiffer, Sy*p'rsia irr Applied Math' conformal mappt'i"' i'ot,-"|^tlt ' 8t1956) , g3-113'MR 20-157 l24l in conproblemsand veriationalmethods Ext'eium ' M Schiffer, 1259. formclmapping.Proc.Internat.CongressMatlr.1958,pp. 2||-231'.CambridgeUniv.Press,.N.*York,1960.MR24A-612.

of in thetheory methods $;rlh?i;,?t;lii,icationsof variationot ' 1260. 1958,153pp' MR 20-157tz4l mapptr;.il;araw-Hill, conformal

Mapping cnd D' C ' Lectureson Conformat l26L Schiffer,M'; Spencer' ExtremgtMethods.princetonLectures,|g4g-1950.[59] problew for multiplyC' Tite coe'fficien't 1262.Schiffer, M'; Sptttt"p' 362-402'MR of fvfali''"'2 (2) 11950)' connecteddomainr. Ann.

1 2 -1 7 1 . [5 9 ] d -^* ntrrc /' n vnri ati onol variati on D' C' Some remarks Spencer' M'; of a Schiffer, 1263. ,onn,"ed domains' Proc' mutriply to applicabie methods ,C. S y m p ' 1 9 3 - 1 9 8 ' N u t ' B u r ' o f s t ap n i ' ' A p p l ' M a tMR h ' S e|4-143.|241 r'No'18'

iiqszl. U.S.Govt.Print.ofti.., w",t'., Sur' puicttonati of FiniteRiernsnn C' D' Sptnto' M'; Schiffer, 1264. 16-461't59l 1954'MR faces'Princeton' in ,on,o,iot mayyingof schiichtfunct265.Schild, A. on a problem MR 14-861'[6' .-,o(r953),4-7-51' tions.proc.Amer.Math. soc 1 0 ,1 2 ,1 9 ,3 1 ,3 9 1

FUNCI'IONS (PART I) BIBI-IOGRAPHY OF SCHLICHT

83

Proc' of functionsschtichtin the unit circle' schild,A. Q,r17cluss 1 1266. l 2 o .M R I 5 - 6 9 4 . 1 4 , 6 , 1 2 5' 'l 9 ' A m e r .M a r h .S o c .5 ( 1i S q ) , 1 1 5 321 Proc. claslof univalent,starshapedmappings. a on A, , Schird |267. . , 6 ,l 0 1 1 , 1 5 , l 5 1 - 7 5 7M. R 2 0 - 1 0 4[ 4 A m e r .M a t h .S o c . g ( l g i s, 7 l ' 7 ,2 7 ,2 ) , 31 , 3 2 , 3 6 ,6 3 1 of annuli-Thesrs'Stan, L. The,onior^al mapping 126g.schmittroitr ford, Univ., 1954't59l | 2 6 g . S c n o l z , D . R , s o n t e m i n i m u275-zg9' m p r o b lIVIII e m s15-802' i n t h e t[59] heoryoffuncJ. Math. 4(195+1, tions.Pacific |2,|0.Schottlaender,s.DerHada.mardscheMultiptikationssatzund weitereKonipositionssatzederFunktionentheorie.Math.Nachr. MR 16-346'l41l l1(1954) , 23.9-294' potenzreihen die im Innern des Einheitskreises r27r. Schur, I. 0a* beschriinktsind.Jour.furreineundangewandteMath., |47(|g|7\,205-232;1a8(1918),122-|4 F M 4' 667(1945)' _475.t59] of5 .Math J' Amer' poiynomials' Fab* On lZiZ. Schur,I. 33-41. MR 6-210.t53l theoremsand criteriaof lZ'73.Schwarz,B. Comptei non-osciltation 80(1955), 159-186.MR Trans.Amer. Math.. Soc. univalence. l7-3',10. [4' 31] , serrcs. of secortdordergeometrrc sutns partiar The . M Schweitzer, r274. D u k e M a t h . J . l 8 ( 1 9 5 : r ) , 5 2 7 _ 5 3 3 . M R 1 3 - 2 3 . t 5 9 ]Amer' functions' theorem for univqlent 1275.Scott,w. T . A coverintg 391 go-g4. 20-877. U9, gsil, MR Math. Monthly 6a(1 |2T6.Scott,w.T.CommentonapaperofC.Utuqay.Proc.Amer. p' 395' MR 2l-662' t19l Math.Soc.10(1959), of clunie'Acta' Fac'Nat' univ' Com1277.seda,v. A noteto Q'p'Qper Russiansummaries)MR enian. 4(1g5g),zss-zoo.(bzech and 23A-56.[5e] bei konfornten Ab1278.Seidel, W. Uber die R'dnderzuordnumg Zbt',1-19' U' z', 3',6', bitdungen.Mat' Ann' L04(193i),182-2131 0 , 2 2 , 3 7, 4 6 ] l of univalentfunctions' Bull' lz.lg. Seidel,W. On the order of growth A m e r . M a t h . S o c ' 4 2 ( l q g 6 ) ' 3 3 5 ' F M 6 2 - 3 ' 7 9 ' 1 6 2 i analytic of functions 12g0.Seidel,w.; walsh, J . L. on the derivstives univarenceand of p-valence. in the unit circreand their radii of Trans.Amer.Math.Soc.s2(|g42),|28_2|6.MR4_2|5.[3,15, 1 8 , 1 9 , 2 2 , 4 2 , 4 1 ,6 2 , 6 B i transform representalz8l. Seshu,S.; Seshu,L. Boinds antl stielties Matn. Analysis and Appl' tionsfor positive,ri functions. _l 3(1961 ), 592-604.MR 25-800' t59l

b--

E4

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

ond approximation by Generarizedderivatives E. w. g37)' 84-128' zbl Sevrell, r2g2. Soc. tranr. 41(l rnruit,. Amer. polynomials.

O:" r283iffii

sci' Acad'sinica furrctions' thedisto\ti?' :{:'!!"!^t MR 15-948't9l

209-212' Record4(1951)' yunrtions' J' chinese of schriilr't ,oejicients tne on T. rzg4. shah, M R 1 7 - 1 4 1U' 7 ' 3 9 ' 5 4 1 M a t h .S o c '( N ' S ' )l ( 1 9 5 1 ) ' ? 8 - 1 0 7 ' MR l2S5.shah,T.ontheproductofm appin g r a d i3(1953)' i f " r . ? . s yl-7 s t'e m ofnonsi"itu tviattr'" doniairiL--e.iu overlopping 17-141.124,261 luncthe theoryof univalent

1286 n -t+rv,n, 53l 2'vlR k:i;:;,,J{^!iJ"{1{;:\,':roi_' ?,lX? prcductof themopprisradiiof lol.overlappingdo-

t2g7. Shah,T. The il-lo. MR l7-142'l59l Marh.Sinica5(1955), ' Ac' mains.Acta functions ,lroo^ of anatytic i"*, it moi)ii tn, on . T r 2gg.Shah, $g-4s;:tcnin.re. Englishsummarv) ta. Math. sinicastiiisll of convexdomqinsin the p.roperties l*;"')t;ll],rring 421^ffir1,t r28s. e.." Math. Sinica7(|957), *ippi,s. confo,^oi of theorl, ' t9' 241 MR 2J-?89:-10 English 432.(Chinese' "'**u'v) - l,/2 is theradiusof superiority number(3 1290.Shah,T. Goluzin's insubordination.s.i.Recordo'11(1957),2|9-222.MR

oi

tzs| 3ffit: \,

dination' Sci the t1!i\'^:l ::p:::'l?-,' {, i"!r1r tll yg-133' MR 2o-r074'

the Record(N'S') 1(195;jt' of convexcomainsin properties covering some MR rzgz.shah, T. s.i. sinitu 7(1958)'816-828' iipi,ng. confor*rl of theory

ofsubordinainthethecrv '"*' i\'-llotities 3ilt1?i.l'3;11;?X" tzs3

tion.Acta.Math.si,'i.u8(1958),.arl&-+t2,.(Chinese.Engiishsum-

u' 17'l9l ,nuruivrn 2i-1350' tofunction' spaces rineor H. s liitiiirroi, of normed r2g4.Shapiro,

Arbor' theoreticextremalprobtems.l-",cturesonfunctionsofacomplex u"iu. of Mich' Press'Ann pp .lgg-44.'Iire variable,

tzss i?i: t5

t"";?l';':i s' Adn^bounded schticht f uncticn2Zl o ?to', ==r, t19' z(rgse eis-e77.MR 20-1074'

), in Mati. vancement functions.Advancement of schricht coefircients tne on S. 1296.shich, 20-968't17l . sii-e01. (chinese)MR in Math. 3(1957) saddlesurfaces isoprri^riii inequarityfor to ' ce'rrant' the on . M shiffman, F r2g7. and Essayspresented u,ith singularrrirr.-sioai., 9-303't59l irl+al, r;s:-tq+' MR

(PARI' i) BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

E5

l 2 g g . s h l i o n s k y , H . G . o n e x t r e n t q l p r o b l e m s f o r dDokli J f e r Akaci' e n ; i a bNar'rk lefunctionals in the theory iy unfrotint funclicns. (Russian)MR 19-738. 124,601. sssR (N.S.) 113(19s7):280-282. SeeSlionskii' Amei ' mapsof circlesinto con'"exrcgions' l7gg. Shniad,H. on analytic Math-Mon.57(1950)'473-474'MR12-401't10'151 1 3 0 0 . S h n i a d , H . C o n v e x i r y p r o p e r t i e s65'l-666. o f i n t e g rMR a l m15-ll2' e a n s o fi3l analytic paciric J. iurutrt.ltr953), functions. potenzreihen;nit monotoner Koef-fizientenfolge' r301. sieron,S. ilbe, A c t a L i t t . S c i . S z e g e d g ( 1 9 4 0 ) , 2 4 4 - 2 4 6 . M R | - 2 ; 3 . [ 4dans , ? 2 ,le 39| lesfonctions univalentes,atg^briques sur L. Siewierski, 1302. demi-plan.Bull.Soc.Sci.Lett.Lodz.Cl.IiIMath.}iatur. 57] 7(1956),No' 4' l7 p ' Zbl 90-291'[9' l303.Siewielski,L.surlavgriqtionlocaledesfonctionsunivglentes, a l g e b r i q u e s d a n s l e d e m i - p l a n . B u | l . S o c . S c i . L e t t .57] Lodz.Cl.III g(lg5Zi, No. 3, 16 p. zblgo-291. [9' Natur. Math. Sci. extre,rtalesdans /esfamilles des 1304. Siewierski, L. sur resfonctions dons le demi-plan' Bull Soc' fonctions univalrnrrr,'o4AOrfques Natur. 8(1957),30 p ' zbl90Sci. Lert.Lodz. cl. rir sii. Math. ? 9 2 .[ 9 , 5 7 ] (Jnivalentand multivolentfunctions' Math' Student 1305. Singh,'S.Ii . 30(1962) ,79-90. MR 26-743' t44l 1 3 0 6 . S i n g h , S . K . ; S h a h , s . M . o n t h e m o x i m u m f u n c tl2l-128' i o n o f a MR 22(1954)' meromorphic function Math. Student 16-459.[9' 16] l30T.Singh,Y.Interiorvariationssndsomeextremalproblemsforcertainclassescfunivalentfunctions.PacificJ.Math.T(1957)' 1485-1504.MR 20-20' 122'241 problems for o new classof univalent 1308. Singh, V. Some extremil 7(1948),gtt-gzt. I\{R 20-771'u5,17 ' .frnctions.J. Math. Mech. 241 coefficients' of the bound1309. Singh,Y. Extremumproblemrf?'the edunivalentfunctions.Proc.LondonMath.Soc.(3)9(1959)' 24',?0',391 3g7-416.MR 22A(l)-18' t17'22' and coefficients of bounded I 3 10. Singh, V . Grunsky inefuatities Fenn' AI No' 310(1962)'22 schlichtfunctions. Ann. Acad. Sci' ' 14,221 PP. MR 26-2'77 ,c.^^^-h,,tn Uspehi conformal mapping of nearby-regions' onv . 1311.Siryk, G. l)' 57-60' (Russian)MR 19Mat. Nauk (N'S') 11(1956)'No' 5(7

2s8.[5el univalentfunctions' 1312.Stiottttii, G. on finite sumsof bounded -709 MR 15-516' 707 , Dokl. Akad. Nauk SSSR(N'S') 93(1953)

b*--

86

BIBLTOGRAPHYOF SCHLICHT FUNCTIONS

u 6 , 2 0 , 2 24 , 31

univalent functions'Dokl' 1313.Slionskii,G. on thetheoryof bounded MR 18(Russian) Akad. Nauk SSSR(N.S.i ril(1956), 962-964' 7 9 8 [. 9 , 15 , , 2 2 , 5 86, U problemsfor differentiablefunc1314.Sii""rtii, G. on the extremal vestnik Leningrad' tionslsin the theoryof univalintfunctions. MR Englishsummary) No. li, o+-s:. (Russian. Univ. 13(1g5g), 20-77r. t24l schtichtfunctions.vestnik r 3r 5. il";rl;i, G. on thetheoryof boundeti (Russian' EnglishsumUniv. l4(1959i,No. t 3,42-51' Leningrad 't221 nrarY)MR 22A(l)-455 L. N ' On a problemof-thetheorYof univalentfunc1316.Slobodeckii, 235-238. MR t;o;ts.Dokt. Akad' Nauk SSSR(N'S') 92(1953), 1 5 - 4 1 3t .9 , 1 5 ,5 8 ,6 0 1 desfonctions univalentes' r3r7 s;;"k',-L: contribution i la theorie CasopisPest.Mat'e2lg32)'l?-19'Zbl6-&'14'6'10'17'36'38' 421 for the argumentof an analytic G. S. on someestimates E*0, 1318. function.Dokl.Akad.NaukSSSR(N.S.)92(1953),7||-7t3. MR 15-613't59l (Russian) ihrorr* in functiontheo'';''Izv' Vyss' 1319.Spak,G. S.,4 coverin'g 218-223'(Russian) . Za,,ed.Matemulitu(1959),No' 1(8), Ucerrn MR 23A-731.[l , 19,221 aprv s1 Jor the modurusand rear r3zo'$0"[-o. s. some estimates pseudo-positivefunctions.Izv.Vyss.Ucebn.Zaved.Mat.|9o2, -lzo.6(31), 148-154' 12,15' 561 |32|.Specht,.E.J.Estimgtesofthemappingfu nctiongndits nearly circular regions' derivativesin conformal mapping of ' t59l MP' 13'337 Trans.Amer.N{ath.Soc.7l(1951),183-196' valentfunctions' II' Trans' 1322.Spencer,D. c. on finiteiy meon 2-82 13,17,33i Amer.lviaih.Soc.+girg4oi,418-435.MR ' i ' Lonidentities , D. c. I'roteon ,o*,, fun'ction-theoretic 1323.Spencef 2-82' 13' 271 a -don Math. Soc'15(i940)'84-86'MR Proc' Nat' Acad' Grunsky' o-f inequatity an on c. D. 1324.Spencer. 616-621'MR 2-79' U8' 191 Sci.U.S.A. 26(1940), valentfunctions'Proc' London 1325.spencer,D . c. on finitely mean 16, l'.i' 18'3],45' Niath.Soc.Q) 41(tg+z),iot-LlLlvIR 3-79.[3,

s2l in onalytic transformations' J ' 1326. SPen;cr, D. C. On distortion g4l), 124-126'MR 2-186' U6' Math. PhYs.N1ass.Inst. Tech. 20(l 1 9 ,3 3 1

FUNCTIONS (PART I) BIBLIOGRAPI{Y OF SCHLICHT

87

of Math. (2) one.valentf;;ictions. Ann. mean on C. . D |377. Spencet, 16' 17' 19',27', 331 42(lg4l), 614-633'MR 3-78' tl5', iS2S.Spencer,D.C.Note.onmeanone-vqlentfunctions.J.Math. Fhys.Mass.Inst.Tecrr.2l1lg4z),i78_188.MR4-138.[331 |32g.Spencer,D.C.Someremarksconcerningthecoefficientsof schlichtfunctions.J.Math.Phys.Mass.tn't.Tech.,2I(|942),

54i 63-68.,rnn4-76.t16, l7 , 42',

identity.Amer. J. Math' A function-theoretic c. D. Spencer, 1330. 461 ' , t47-160'MR 4-137 [33' 55(1943; ionfornrut mappins' Buti' i! problem, Somi C. . D Spencer, . I 3 I3 417-!39'MR 8-515'l4/'l Amer. Math' Soc'Sltrq+T' mappingsof the problem1or schlich-t t332. Springer, G. The,orlitfrni e x t e r i o r o f t h e u n i t " c i r c l e . T r a n s . A * . ' . M 5a3t h' 5 .Soc.70(1951)' 1 6' , 1 7 ' , 2 4 ' 2 5 ' , 2 7 ' , 8 1 t 5 ' 1 3 2 4 ' t n ' M R 421-450. FunkHi)ueschrichter derkonvexen Extreme'p'unkte G. Springer, 1333. t9', 15',17', i{R 16-1011' 230-232. fionenMath.Ann. t)g0955),

u:t1:*"!:::KX'ri:i'-'::; "#;o;{ , . onthemean 1334.3?;"1-l;,i'i'*. derivatives,Riv.Mat.Univ.parmaS(1957),361-369.MR21_ 1 0 6 3 .I 5 9 l .^rAr rRiesz' J' Loncl o n M a t h . S o c . P ' On a theorem o'f M' Stein, 1335. 8 ( 1 9 3 3, 2 ) 4 2 - 2 4 7 'F M 5 9 - 3 2 5 '[ 3 1 Proc' methids in conformsl mapping' 1336. Stone,M. H . Hitbert-rpo,, pp' 409-425' spr.., (Jerusalem1960), r-in!u, Sympor. Internat. JerusalemAcademicPress,Jerusalem;Pergamon,oxford;1961.

MR 25-39.t59l

andunivalent betweentypicary-rear 1337.Streric,s. I . on a connection(N.S.l nig57) No' 3(75)pp' 2llNauk functions.uspehilurut. 13' 4U ' 220.(Russianirurn 19-643'[4' an.alvticin o ctrc:k. functions 133g.Strelicas,S. Some^irop,irr,:;{ Daiuai. Mat' Fiz' chem' Mokslu vilniaus valst. univ. Moksl0 MR 22A(2)summary) Russian (Lithuanian. 6,7_71. Ser.4(1955), 2 0 9 3 . [3 , 4 , 1 7, 541

. ?,'(z) ,-, ..sl n* der Frerl i nhuns d, dA SS unter ,tor Bedinbung Ar.cf 1339.Stroganoff,w. G . \be, den f(z)diekonformeAbbildungerne,st.ernartigenGebietesaufdas Mat' Inst' z-Ebene tiefert' Trudy innere des Einheitskreisesder S t e k l o v a 5 ( 1 9 3 4 ) ' z ' + l - Z S g ' Z b l 9 - 1 7 3schlichten ' [ 6 ' 1 5 ' 6 8Funktionen' ] Th-eorieder 1340. Strohhhcker,E. B'eitros,,u' Math.Z.37(|933),356-380.nbl7-2:I4.|2,6,10,15,17,|9,29,

u3'u?rll|"r*, Einfachzussmmenhangender Abbitdung 1341i?;jr?;

E8

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

Bereiche.B.C.Teubner,LeipzigandBerlin,lgl3.FMM_755.||, 1 0 ,3 7 1 |342.Suetin,P.K.Faberpolynomials-forregionswithnon-anolytic boundaries.Dokr.nr
n I |343lliJ:; :t8l" ontheorcter or?y,'?o:',:: !'S{,?-"RK'Ki'J moppingsincloseddomqins.pot.t.Akad.NaukSssR(N.S.) 22-23'MR r'7-956'122'60'621 107(lqsz),

1 3 4 4 . S u v o r o v , G . D . o n t l t e c o n t i n u i t yicaO' o f u n i vNauk alent.m appin gsofarSSSR N'S')

bitrarv closed ao*'oin' "' ?"-kl: t59l M^R. 108(1956 1, ltl -179' (Russian) .18-724' mapptngs in of distances un.ivarent 1345.SuvoroV,G .D. on iistortton +S(gz)(1958),rsq-180'(Russian) sb. N.S. regions.rurui. of ctosed

1346sj.HrL.*31

,,on distortionof correctionto the srticte

distancesinunivqlentmoppingsofclosedrlg|ns''.Mat.3b. (N.S.)48(90)(1959),25|_252.(Russian)MR23A_51.u6] andareaprincipl,'f?IQ-quasiconfor|34,7.SuvoroV,G .D, Thelength 126',7-1269' sssR 140(1961), mal mappings.ooti. ,i,t uo. Naut (Russianjvri 24A-372'[7' I5'z4l etner fur die Ableitungen beziehungen O. Ungleichtheits 1348. Sz6sz, Funktion beschrankte potenzreihedie eine im Einheiik"i" FM 47-274'll5' 22',6ll g7t9t2)),303-309. darsteutMarh. z. abdie den Einheitskreisschlicht r34g. sz6sz,o. uber Fuiktionen bilcten.Jber,Deutsch.Math.Ver.42(|932),73-75.Zb]t5-108. com,*\^r:?':.2ln,n, meonsof Fourier seriesand Riesz cesdro 1350. p o s i t o M a t h e m a , , i c a T ( | 9 3 9 ) , | | 2 - : 1 2developments 2 . M R 1 - 1 3 8and . t 5 of 9] of hormonic sums p-orifci e tt On O. l35l . Sz6sz, pcwerseries.T,ans.Amer.Math.Soc.52(|942),|2_7i.MR4_17.

^t o,' o, kiewicz' E'; za19rsr
starlikefunction,. MR 2G980' [5' 6] and English.summaries) l 3 5 3 . S z e g b , G . U b e r o , t t , o g o n a i e P o l y nMath o m e' dZ'i e9(1921)' z u e i n e 218-270' rgegebenen Kurve der kompterr:n-ibon' sehoien' FM 48-374' l59l uber die emetn staz von J. H. Grace zu Bemerkungen G' 1354. Szego, Math' Z' 13(1922)'28-55' wurzein algebraischir Gleichungen' -ver' FM 48-82. [59] Jber' Deiitsch' Math' Minimatflachen' Retative 1355. Szegci,G. 3l(1927't,4l-42' t59l

)

BIBLIOGRAPT{YoFSCHLICHTFUNCTIcNS(PARTI)E9

Form von einer quadratischen Maximum das nber -ver' G. 1356.szego, Jber' Deutsch' lvtath' vuroniirlichen unendlichvielen 3r(rgzz\ 85-88'FM 48-490't3lr;tit endtichvieienverschiedenen potei,izrrih,i ,'i.-tiuer ' FM r35.r.Szegb -8. Preuss.e.aJ. wiss. (lgzz)', 88-9! S. Koeffizienten.

E:,'.'::::'K!:,'*J^:{: eine uber 38iliil 5:'Abbitarngrn 22(1923)' :"','rlif{i:,;,i{ 1358 sitzber.B;;. Math' Ges' schtichten r35eI;H

. z. z3(rszs)' Matn :n #t rl,T: seti;onA. MarkofJ.

Ls-61. FM 5r-97' t59l

l 3 6 0 . S z e g o , G . T . u r T h e n , i e d e , s c h [6' l i c h'o' t e not) Abbildungen,Math.Ann. --^i-nthe sectionsof 100(1e;t,lss-zt 1' FM 54-336' concerning investigations ,,,,n, Some G. 1361.Szegti, p o w e r , e , i e , a n d r e l a t e d d e v e l o p m e221 nts.Butl.Amer.Math.Soc.

12'20' of 4z(iqrii,ios-szz'zbrr4-3s2' sequences multiply monoto-nic

power ,;;;r; with 39] t362. szegii, G. 8(194D: isg-so+'MR 3-76' [4', cr J. Mrth. Duke coefficienrs. t'heinteriorof an ellipseonto confor*ot'iopprni G. Szeg6 , "t r363. MR 12-401't5il . sl(t950),4'.74-478' circte.Amer. Ir{ath.laon and rineardifferentiarequq' schticht functio'nis ak. choy-T Taam, 467-480' 1364 r.n.frt'Analysis4(i955)' nat. r. orailr. secona of tions

n:{'^'21:Jio;l'Zor3',':;r" " JI?" " :!li:-h' ,365?:iff;l;i : .P 2: 14,6'10'201 56-e85' FM is-eo. 33ii;;dj, J. Math. rohoku

Rado' Jap' eine'rArbeit von Herrn zu Bemerkung s. 1366.Takahashi,

J . M a t h . ? ( 1 9 3 q ) ' r o t - t e " z ' n vund,hinre-ichende r 5 6 - 9 8 6 ' u ' 6 ' 1Bedingung 0'371

notwendige |367. Takahashi,S. uaer aie Proc' Imp' Acad' Einheitskreises' des aaittaung fur dieschlichte 431 ' Zit 6-05'14' 6' 11' 20' ,344-34:t von Jap.8(1932) xoifftztentenabschatzungen ' 6L';'S' 1368.Takahashi' -arc Imp' Acad' Jap n Potenzrriiin ' Proc' ungeradenschlichte 39' 42' 45' 521 ' 9(1933),l-2' zu e-ie2' t8 ',17', Funktionen Bemerkungeniber schtichte 431 1369.T akahashi,s. zwei juo 9(1933),iot_+e+.Zbl 8-168. |42, Proc.Imp. Acad.. schlichten einer ungeraden Abschnitte FM 1370.Takahashi,s. uber'die -Math. i;.. Jap'(3)16(1934)'7-15' pro.. phys. potenzreihe. 451 the 60-283.[6, 10' ll' 12' 20' and sufficientcondirionfor necessary the on S. 1371,Takahashi, iigular tn the unit circle' function analytic on ' multivalencyx FM 62-376 io..-lup ,3f iitrqldl, 353-355. proc. phys.-rurutr,. [4, 14]

,,.:,

b---.

90

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

of an anaryticfunction' Proc' s. on the murtivarency 1372.Takahashi, Imp.ecaj.Jap.l2(1936),59-60.abl|5-7 1^.[4'14] mappingsin severalcomplexvariables' univoleni S. Takahashi, t373. MR 12-818.[59] g,^ Ann. of Math. (2) 53(lt5 iu-+71. of schlicht of the coefficlents 13j4. Tammi, o. on the maximalizqtion sci' rennicaeser' A' I' Math' and related functions.Ann.Acad' -Phvs.No.l14,51pp'irqszl'MR14-366'[6'15',17',23'24'29' of schticht coeffic-ients o, certaincombinationsof the t3i s fihr,l3. f u n c t i o n s . A n n . A c a d . s . i . F e n nli5c 'a1. S7 .' 2 ' . 3A'5. E4 .' 6M8a1t h . . P h y s . N o . 1 4 01 3p p ' ( 1 9 5 2 )M' R 1 4 - 7 4 OU' 2 ' solutionsof Lowner'sdif1376.Tammi, o . on tnr rorfftcients-o1t.n' I' Math' Acad' Sci' Fennicae'Ser' A' tii. equation. fercntial -Phys.No. r+e,7 pp' (1953)'MR 15-302'Q4l of the coefficienth of bound1377.Tammi,o. on the maximalization r'ennicae Ser'A' I' Math' sci' functions.Ann'Acad' ed schlicht '24' 541 - P h v sN. o ' 1 4 9 'r A p p ' ( 1 9 5 3 )M' l 1 5 - 3 0 2U' 7' 2 2 ' 2 3coefficient to the domainsberonging r3Tg. Tammi,o. on the ,itri*or Sci' Fennicae'Ser' functions.Ann. Acad. ot of boundedschli;:lut A . I . M a t h ' - P h v s ' N t ' ' 1 6 2 ' 1 2 p p 'bounded ' ( 1 9 5 3 ) 's;rtricht M R l 5 -functions' 516'122'211 coefficients the on . o 9f r37g.Tammi, Tolfteskandirraviska"Matematikerkongressen'Lund'(1953)' ' 122'421 2g7-30r(1954)'MR 16-347 schlichtdo' ^opping of symryetric 13g0.Tammi,o. on theconformal i. i. vruitt'-Phys'No' 173'12 mains.Ann.Acad.Sci.Fenn.Ser. 421 ted pp. (1954)'MR 16-233'122'24'39' schlichtdomainsof bouna ,y**,tric on Note o. 1381.Tarr^mi, b o u n d a r y r o l a t i e n ' n n n . A c a d . S c i . F49' e n541 n.Ser.A.I.No. 39' '23' l7-5gg' t17 MR pp' 10 198(1955) Fac.Sci. coeffiiientthe.orem-Rev. 13g2.Tammi,o. Noteon Gutzmer,sg-i1' (f"t kish suinnary)MR 20Univ. IstanbulSer. A22(1957), 8 7 7 [. 1 , i 7 , 4 9 1 Polon' functionl. luil. Acad. o. on bcundedunivarent Ta^nrr.i, 13g3. (Russian sum' z(iqsg),413-417 Sci.ser. sci. Math. Astr. Phys. m a ry ) Z b l 9 4 -4 9 ' 1 2 2 ' 291 . :,-a:^- in t- the th,t thenr! i honrv of of tuni-!arrrmi,o. on a niet',hoiof symmetrization 13g4. Sci. Fenn. Ser. A' I' No' 302' valeritfunctions. irrn. Acad. ( 1 9 6 1 ) , 7 p p ' M R 2 4 A - 3 8 ' 1 2 4 1 - - , : - ^ t t n n i n t h o crass s*. ooff unt' in the r t n s cS extremerization of mcthod a on o. Tammi, 1385. ,',ulentlunctions.Ann.ecaa.Sci.Fenn.Ser.A.I.No.320(1962), 6 PP.MR 2s-426'1241 distortionunderq schlicht boundary p. Rerative M. 13g6.TamrazoV,

BIBLIOGRAPHYoFSCHLICHTFUNCTIONS(PARTI)91

c o n f c r m a ! i n a p p ; n g o f g d o u b t y c o n n e c t e(ukrainian' d d o m a i n . Russiatt Dopovidi (1962L 338-340. nsi Ukrain. Nauk Akad. MR 26-743' t60l and Engti,t' mapplngs "t*maries) the'ry' of i'"li''h' ccnformal On-i'tie ' M P' 1387.Tarnra,ou, ofdoublyconnecrcd'.clomains.Dopo v i d i A k a d .summaries) NaukUkrain. (Ukrainian' Russianand English 1962,563-565' RSR

in theunitcircte' anatvtic of H' func'tions ;t:)!e t r388 Yrli? Stoss 19-130'[59] yokohamaMarh.J. alDiol, 4i .5.3.MR ln Acivancernent

sectioniof ichlicfu functiot's' 1389.Tang, i' fn' Math.3(lgsi),468_471.(Chinese.Englishsumnrary)MR20-

t f :;(::!,' Englishsumedisto-:':?: :-!' 478-.484. fi. itJ'i,3l'o'inthMath. " I3e0 ." :: : (chinese' lirqsz )", ":Ti;?#,

vancement 4 '5 8 '6 U m a r YM ) R 2 1 - 2 6 'l g ' l 5 ' 1 6 ' 2 2 ' 2 itrro'rr^-t of Hardybv Banach p.roofsof some New A.E. T,ayror, r39r. S p a c e m e t h o d s . M a t h . r u r u g . 2 3 ( 1 9 5 0 )den , 1 1 5Koeffiz,ienrcn -:t24..MR11_507.t3] zwischen Llngleic:hungen o. Teichmiiller, |392. Pr.urr. Akad' wiss'' Phys' Stizgsber. Funktionri. schlichter 24' 251 ' 363-3't5't9' 15' 17' -Math.Kl' (1938) und quoriionfoime Abbildungen Exti.ernare o. r 393. Teichmii'er, q u a d r a t i s c h e D i f f r e n t i a l e . A b h . p , . 'u ' ' . A k a d . W i s s . , M a t h . Kl' (193t)'No' 22' MR 2-187 t59lder konformen -Naturwiss' (iL" Extremalprobleme 1394.Teichmuller' O' Gcometrie'Dtsch'.Math'6tlg4l)'SO-ll'MR 3 - 2Sci' 0 2 'Univ' U7'271 Fac' verzerrungssa{, fev' r395. Terzio[ru,A. N. uber den ' 3 - 1 1 8Z' b l 3 8 - 5 2 'U 5 l I s t a n b uAl 1 5 ( 1 9 5 01) 1 1 3 9 6 . T e r z i o [ l u , A . N . ; K a h r a m a n e r ' S . E' iRev' n V e rFac' z e r r Sci' u n g univ' ssatzdes Funktionen Argur,tentesder sciirttten I s t a n b u l S e r . A . 2 0 ( 1 9 5 5 ) , 8 1 - 9 0Ubel . r ' n n 1 7 - 8Argument 3 6 . t l 5 , | 7der ,54,68] S' Kahramaner' las N.; A. A' Tcrzioflu, i3g7. univ' lstanbulser' Funktiiien. Reu. F; Sci' 15' analytischen (rurtirt, ,ur"*arv) MR 19-846'[9' 2l(1956) , r4s-153(i;;;).

fra,t"::',t-:::'t#{i;:it"' of continued l?ur., J' S' Univalence 1398. MR 17-1063' iiiqie ), 232-244' Math. Soc. forms.proc.Amer.

on{!.n:li.o!.', "' (r!i r3ee. Ii*, t.'i :'i',t.,o,em :' :'So :if',ff#' {u'.' 13-335' t4l MR ' 2w-205 rtiqsr )' Soc'ill Proc.Londonruruit''

1400.Titchmarsh,E.C.TheTheoryofFunctions.oxford,|932,454

Funk' positiver Entwicktung 140r ?t";f,i,i:3t' u#' 0,, oorrier'sche

hr.-*---

92

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

tionen.Rend.Cir.Mat.Palermo32(1911),|g|-|92.FM42-428.

tzl of schlichtfuncK. c . on a coveringtheoremin the theory Tong, 1402. Record4(1951i,37-4A.Zbl 42-315.u9l tions.Sci. schlichtfunctions'Proc' Amer' 1403.Townes,S. B. A theorim on 585-588'MR 16-25't39l Math. Soc.5(1954), whosereal part is positivein a 1404.Tsuji, M. On a rrsutoi function MR 1l321-329(1949)' unit circte.proc. Japarricao. 2l(1945), 3 3 8 .[ 2 ] equation in the theory of uni1405.Tsuji,M. On Lowner'sdifferential g47), 321-341'MR 10-440' vqlentfunctions' JaPanl. lnattt. 19(l l24l conformal mapping' J' M. ,4 deformation theorem on Tsuji, 1406. M a t h . S o c . l a p a n 2 ( | 9 5 1 ) , 2 | 3 _ 2 | 5 . M R | 3 _ 2 2 4 . |szego's 49| contheorem concerning 1407.Tsuji, M. A rimark on R'ei,ngers jecture.KodaiMath.Sem.Rep.1953(1953),117_1l8.MR 1 5 - 6 1 3U . 9l in o unit On the radial order at a certainregularfunction M. 1408. Tsuji, c i r c l e . J . M a t h . S o c . J a p a n 6 ( 1 9 5 4 ) , 3 3 6 - 3 4 2 . I V I equivalent R16-809.[62] which is conformauy surfice, niema,ni a on M. 1409. Tsuji, spherical area' Comment' to G Riemann surface witi a finite M a t h . U n i v . S t . P a u l 6 ( 1 9 5 7 ) , | - 7 . M R 1 9 - 1 0 4 3 . t 4 6nrcromo-r' ] boundcry behaviour9f .o 141C.Tsuji, M. A theorernon the Phic \un,,tion in l z l ' l7', 16',46',621 3(i960),53-55.MR ize'rz>-l899 oei der cesdro-mittel Konv:ergenz 14r. Turln,'i.- hbe,die monotone Phil' Soc' 34(1938)' Fourier und Potenzreihen.Proc' cambridge

t34-143.Zbr rg-ri. t59l funcin the theoryo.funivarent r4rz. Turkovskii,v . A. o; a theorem ' 189-191 (13)', 6' No' (1959), ticns.Izv.vyss.IJc. zaved.Mat. M R 2 4 A - 3 8 .[ 4 , 1 0 ,1 6 ,1 7 1 valuesof certainsystemsof func1413.Ulina, G. v . on the domainsof of univalentfunc-tions'-vestnikLeningrad tionalsin the classes MR EnglishSUITlIIl0,r-y) No. r,31-54. (Russian. Univ. 15(1q60), . 124,29, 397 22A(2)-965 prope;'tiesof yjllcht functions' 1414.uliman, J. L. Two mapping 9 ',231 proc. Amer. Math. Soc.^ittgiri, es+'ost.MR 13-223'[6' Amer' Math' in Faber poiynomials-Trans' 1415.Ullmatr,J. L. Studies

' zbrT-o' ' ts3l 515-528 soc.q+irqoo), auf mero' des Verzerrungssatz'es

1416.Uilrich, E. (lber eineAnwendung Math' 166(1931/32)' morphe Funktionen. J. Reine Angewandte 220-234. [9' 15]

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

93

Krummungsver' mit ausgezeichnetem r4rj. rJllrich, E. Betr,dtachen h a l t e n . M a t h . Z . 5 4 ( | 9 5 1 ) , 2 g 7 _ 3 2 8 . MlaR troisibme | 3 _ | 2 4 . [espdce' 2,35] de Btoch de les sur c. fonc:,t'ions 141g.ulugay, Conrm.Fac.Sci.Univ.AnkaraSer.A.6(1954),5-1C.MR 1 6 - l o l1 . U e l et de la lesfonctions de Bloch de Ia premibre iur i. ullrich, l4lg. A' 6(1954)' comm. Fac.Sci.univ' AnkaraSer' secondeespdce. 1 1 - 1 6M . R 1 6 - 1 0 1t11 9 l | 4 2 0 . U t l r i c h , E . o n t h e-88' c o n s t ui6ntC . CI 'o t19l mm.Fac.Sci.Univ.Ankara 101 MR Ser.A. itr gs4). 77 comnr. Fac' Sci' Broch-Lqndauconstants. r42.r.urlrich, E. on the (Turkishsummary)MR Univ. Ankara Ser.A. 7(1955).233-252. r7-472.tl9l of schworz'slemma'comm' generalization 1422.Ullrich,E. No/e on a 1-5. (Turkishsummary) Fac.Sci.univ. Ankal s.r. A. 8(1956), MR 1e-736.t5el of the third kind and the constant 1423.Ullrich, E. Bloch.functions U . P r o c . A m e r . M a t h . S o c . 8 ( i 9 5 7 ) , g 2 3 _ g constants 2 5 . M R 1B' 8 - L' 736.[16,19] Btoch-Landau the values'of exact The . E, 1424.Ullrich, J . R e i n e A n g e w . M a t h . l g g ( 1 9 5 8 ) , i 8 8 _ 1 9 1 . M RJ. 20-87,7.[19] of schrichtfunctions. Reiile coefficients tne on E. Urlrich, 1425. 2 1 - 1 1 9 5[ 3. ,l 5 ' 1 6' \ 7 , 4 2 ' 5 1 ' , A n g e wM . a r h. 2 0 2 ( t g 5 91i ;- 5 .M R 681 J' ir, the theoryo.fschtichtfunctions' 1426.U'rich , E. on inequarities ReineAngew.Math..202(|959),6-8.MR21-1195.[6,15,16,|7, 4 5 , 5 2 , 5 4 , 6 76,8 1 zeros' functionswith sssigned of murtivarent T. A crass 142,7.Umezawa, 13'14' proc.Amer.Math.soc.3(lg52),gti-szo.MR 14-260'[6, 1 5 ,1 7, 3 6 , 4 0 ,5 0 , 6 3 ,6 5 '6 6 1 convexitt oy.edi.rection'J' Math' 1428.Umezawa,T. Analyticfunctions Soc.Japan4(1952)'PI-ZOZ'MR14-461'[4'12'4 ll of analyticfunctions'J' Math' multivalency the on . T 1429.Umezawa, Soc.Japan4(|952),279_285.MR14_ 859.|4,6,10,14] of orderp in onedirecstarrike Anarytic T . functions 1430.umezaw&, MR 14-859't15' l7 ',39', tion.TohokuMath' l' kr 952)'264-27',7' functions' J' Math' of muttivate,nt 1431 th::lwa, T. on thecoefficients 49' 511 ni-tu' MR 15-302'U3' 17' 39' Soc.Japan5(1953); 1 4 3 2 . U n r e z a w & , T . S t a r - l i k e t h e o r e m s s n d cMR o n v15-947 e x - i i k' e[4' t h48] eoremsinan qnnulus.J. Math. Soc.Japan6(1954),68-75' 'f. functions'Duke of m'e:romorphic 1433.Umezawa, The coefficients ,3 6 '4, 0 1 1 5 - 9 4' 7t 1 6 ' , 1' 1 M a t h- J . 2 r ( 1 9 5 4 :) s, i - l o l ' M R

94

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

of univolentfunctions' Tohoku 1434.Umezawa,T. on the theory M a t h . J . 7 ( 1 9 5 5 ) , 2 1 2 - 2 2 8 ' M n 1 7 - 1 0 6 8 ' 1 4 ' , 9 ' , 1' 0 Proc' ',14',601 functions close-to-convex Multivalenil' T' 1435.umezawa, Amer.Math.Soc.s(l957'1,geg-uq.MR19_846.[4,5,7,|4,|5, 1 7 , 3 8 6, 4 ,6 5 1 Rsndvrzerrungbei konformer Ab1436.unkelbach, H. uber die b i l d u n g : . V t a t h . Z . . 4 ? ( | 9 3 8 ) , 7 3 9 - 7 4 2 . 2 b | Funktionen | 8 - 2 2 5 . t 4 6an ] vorrat anarytischer 1437.unkerbach, H. Llber den grassenFunktionswerten.Jber.Deut'sch.Math.Ver.49(1939)' 38-49. Zbl2l-143' [6, 10' 19] beischrichterkonformer 143g.unkelbach,v^. Uberdie Randverzerrung MR 2-83. [6, 10, 46] Abbitdung.Marh. z. ie!940), 329-336. IJberdieApp,ozimationschlichterkonformerAb1439.unkelbach,H-. speziellersternigeroder bitrlungendurch t onsrurnteIterat|onen 63-70'MR . z. 58(1953), konvexerkonfor*rr^bbildungen.Math 1 4 - 8 6 1[ .1 5, 2 2 1 o-fa univalent B. M. On theorgumentof thederivativ_e l4o. Urazbaev, Ser' 56(1948)' KazahssR star-shoped function.Izv. etua. Nauk 631 .2, |02_|2|.MR 13-546.[6, 15, Mat. rr,r.r' lc :ur le ilftirbme de NI' Borel dans l$L Valiron, G. Recherches 5't-97' Acta Math. 52(1928), theoriedes fonctionsmeromorphes. FM 54-348.[se] de fonctionsentibres d,univarence 1442.variron, G. sur resdomaines d , o r d r e n u l . C o m p o s i t o M a t h . 3 ( 1 9 3 6 ) , de | 2 9Riemann _ | 3 5 . 2 bdefinie ||4-266.|28| surface ls de rn Division feuitlets 1443.Valiroo,G . Appl' 9(19) (1940)' psr w : (e' - l)/ z + h". J. Math' Pures 339-358.MR 2-3s8.t59l ' Math' Ann' gttfvatureof level curves 71rs on s. Verbiunsky, I 14I . 125(1953 ),'472-47o'IIR 15-206't35l c. R' u,ni,arenles. fonctions anguraire'dei d6riv,ee ra sur c. visser, rM5. ';z+-s25.Zbl l0-120. [461 Acad.Sci.paris 199(19341, desfonctions univalentes' 1446.Visser,C' '\ur la i6'fuA' ongulatre Akad.Wetensch.AmsterdamProc.3S(1935),402-4l|,Zb|

r2-2s.t46l

lM7. Visser,C. Sur la deriveeangulairedesfotlctionsunivalentes.I|. ' Zbl l1' AmsterdamProc. 38(1935)'618-627 Akad. Wetetrscn 407' i46l 'tffatt k-fach symmetrisch'er spezu 1448. Waadeland, H' Uber einen .sch|ichtcrFunktionan.Norskevid.Selsk.Forh.,Trondheim

l9' 391 MR 16-916'tl7', rsi-r55.(1955), 27(rg54),

sternfdrmigeschlichte iMg. waadeland, H. uber k'-fachsymmetriiche

(PART I) BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

95

AbbitdungendesEinheitskreises.Math.Scand.3(1955)'150_154. MR 17-25.16,17, 36, 491 einerArbeit von Golusin'Norske 1450.waadeland,H. Bemerkungzu , 2'9-32'I\t'tR! 8-201'U7' vid. selsk.Fcrh., Trcndireim29(\956) 42, 45, 52, 54i satz iber schlichteAbbildungen H. Ein Gorusinscher l45l . waacterand, 15530(1957)' von lyl > l.Norskevid. Selsk.Forh.Trondheim [9, 17,251 168.MR 2A-6(A'. ein kceffizientenProblemfilr schlichteAb\bq . l4sz. Waadeland,H bilCungendeslf l I'{R 20-664'[9, 17' 251 168-170. 30(1957), von scott' Bedeckungssatz 1453.waadeiand,H. Bemerkungzu einem 112-116'MR Norske vid. Selsk.Fcrh. trondheim 32(1959), 24A-370.U7, 541. ncr' (Jntersuchungen uber Aquivalenzklassen 1454.waadeland, H. Tron' Skr selsk' mierter, schtichterFunktionen Norske vid' 541 24A-254'Il7 '29' dheimirqsgl,No..3,47pp' MR I, II' Funktionen. 1455.waadeland,H. uber biichrankteschlichte MR Norskevid. selsk.Forh.Trondheim32(1959),84-91'92-94' 2 4 A - 2 5 4U. 7, 2 2 , 2 4 , 3 0 1 Funktionen.Nor1456.s'aadeland,H. zur The'orieder beschriinkten MR 26-748' 82-85. skevid. selsk.Forh. Trondheim35(1962), 115,22, 6ll

.

, r

a :^ - - ^ r \ T ^ . . V . ^-L

Fractions' New Yo:k' 1457.Wall, H. S . Anaiytic Theory of Continued Van Nostrand, 1948' MR 10-32' t59l curvesof Green's 1458.Walsh, J. L. Lernminscatesand equipotential function.Amer.Math.Month|ya20935),|_|7.t59] l 4 5 g . W a l s h , J . L . N o t e o n t h e c u r v a t u r e o f t e v e l c u r v e s o f G r e FM en's Sci. u.s.A' 23(1937),84-89' Acad. Nat. Proc. furtctictn 63-297. [9' 10] of Green'sfunctions' 1460. Walsh, j. l-. On the shape of level cttrves g37),2a2*213.FM 6-7-296.t59] Amer. Math. Monthrv ++(r traiectoriesof 1461. Walsh, J. L . Noteon the curvatureo.f orthogonal Amer ' Math ' Soc' level curves of Green's functions . Bull ' 44(1938) , 520-523-Zbl 19-271' [59] 1462.Walsh,J.L.onthecirclesofcurvatureoftheimagesofcircles a6(1939)'472-485' undr a conformal map. Amer. Math' Monthly M R 1 - 1 1 1 .[ 1 9 ' 3 5 ] analytic in the 1463. Walsh, J. L. Noteon the derivotivesof functions 515-523'MR 9-23' unit circle. Bull. Amer. Marh. Soc. 53(1947),

u 5 , 1 7 ,1 8 ,1 9 1

96

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

mapping of multiply connected 1464.Walsh, J. L. On the conformal 128-146'MR l8-290' regions.Trans.Amer. vrattr.Scc.82(i956),

t60l | 4 6 5 . W a l s h , J . L . I n t e r p o l a t i o n o n d a p p r o x i m a t i ocolloq' n b y r a Publ'20' tionalfunc Soc' in the complexdomain Amer' Math' tictns

t5el 2ndEd. (1e56)' mapsof multiplyH. J. on canonical Landau, walsh, J. L.; 1466. 81-96' Zbl Trans.Amer. Math' soc' 93(1959)' connectedregiorzs. 86-281.

[59]

.. , , , , - , ) ^ - , r ' x t n t t t , n o ,der A lrder Abreitungl o r Ab' Randverharten das Uber s. warschawski, r46i. Z' 35(1932)' bei koiformer Abbildung' Math' bitdunssfunktion 321-456.Zbl 4-404.u9' 461 at theboundaryin conderivatives 146g.warschawski,s. on int'nisier 310-340'Zbl Trans.eler. Math.Soc.38(1935), formatmapping. 14-267. t59l . ? - . , ^ - - ^ ^ L t i n h r , > r Funk .. , ,, schlichter F r t n k . warschawski, S. Uber die winketderivierten 1469 t i o n e n . C o m p o s i t i o M a t h . 4 ( 1 g 3 7 ) , 3 4 6 _ 3 6 6 . 2 b | | 6mapping -407.t46] method of conformal 1470.warschawski, s. on Theodorsen's o-fnearlycircularregions.Quart.ofApplieciMath.3(1945), 12-28. MR 6-207. t59l regions' s. on conformal mappingof nearly-circular warschawski, l4TL P r c c . A m e r . M a t h . s o c . l ( 1 9 5 0 ) , 5 6 2 - 5 7 4 . M R 1 2 _in 170.[3] of the boundory confor' on-diffe'rentrabttity s. warschawski, r4iz. molmappmg.Proc.Amer.Math.-Soc.|2(|961),614_620.MR

24L-2s3.t59l

DaJ@d' DukeMath' J' series 1473.whittaker,J. M. A noteon the 2l(rg54),571-573'MR t6-232' t59l pour la classedefoncde-Koebe 1474.wiatrowski,P . sur i tn\orbme 10(1959)' bornees.Bull' Soc' Sci' LettresL6d'2 tionsunivalentes

Ne. 14, 13 pp. MR 24A-37' t19] ^ r ,, .- --^)it- Enttr' variation of a function and its Fourrer 14j5. Wiener, N . The quudratic c o e - f f i c i e r r f . s . M a s s . J . M a t h . 3 ( 1 g 2 1 ) , , 7 2 _ 7 4the .FM 50_21i3.[591 quantum from 1476.wigner, E. P. on a classof enalyticfu'ictions (2) 53(1951)'35-6'7' I''{R theory of cottisions.enn. of lvlath'

mapsof convex sequences f9y ordinating factor *rllt;l?.t3],, r4.ti ), 689-593' MR so.. 12(196i

the unit circle.prol. em.i. Math. 2 3 A - 4 1 51. 1 , 2 ,1 0 ,1 6 ,4 i i of certoinentirefunctions' llr47g.wilf . H. s. Therartiusof inivarence l i n o i s J . M a t h . 6 ( 1 9 6 2 ) , 2 4 2 _ 2 4 . } , I P . 2 5 -schiicht 426.t28] of funcfions, coefficients the of Averages ivl. G. Wing, A7g.

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

91

iroc.Amer.Math.Soc.2(|951),658-661MR13-123.||7,20,42, 541 l4S0.Wintner,A.onthe.principleofsubordinationinthetheoryo'f gnal},iicaifferentialequat.ions.ActaMath.96(1955),|43_156.

Studia Funktionen' rheoriederschtichten , $l,i,l;;it*ltirgj r48r ::, i0' l5' 58' 5+] 4(1933t , 66-69'Zbl8-319'[9' N1ath.

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_

-.!

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BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

u , 6 , 1 0 ,I 5 , 2 3 ,4 9 ,6 3 ,6 4 1

images'Acta Math' 1495.Wu, Z. A classof functions with star shaped summarv)MR sinica 7(1957),433-438.(chinese. English 23A-177.16,20,431 potynomials'Sugaku 1496.Yarnaguchi,K. On a property of schticht MR 26-7M' U5' 321 ll(lgsg/OOj,la-g9. (Japanese) of the expanr4g7.yan-sin, cin on the orgumentsof the coefficients sionofaunivalentfunction.ActaMath.Sinica4(1954),81_86. Russiansummary)MR 17-142'[4' 39] (Chinese. of nearlycirculardo' 1498.yoshikawa,H. On the coiiormal mapping , 174-186'MR 23A-329'16' moins.J. Math. soc. Japan12(1960)

4el

die p-wertigen Funkl4gg. Yosida, Tokurrosuke Bemerkungen i)ber gM),16-19' MR 7-288' [9' tionen Proc. Imp. Acad. Tckyo 20(1 1 4 , 1 5 , 1 7 , 2 5 , 4 3 '5 8 1 p-wertigen Funktionen' 1500. Yosida, Tokunosuke Ein Satz uber die Proc.Imp.Acad.Tokyozo(|g4p;),409.MR7-288.[14'15] on the boundaryvaluesof 1501. Yurchenko,A. K.; Durldudenko,L. E. in the circle lzl functions regular and univalent ukrain. Mat. z. 9(1957), 455-460'(Ruscertain spec;al classes.

sian)MR 19-846.16,231 schlic-ktJunc1502.Zamorski,J. Equationssatisfiedby the exiremal MR 18-568. tionswith a pole.Ann' Poton'Math' 3(1956),4r-45. 19,17, 24, 25, 291 star-likefunc1503.Z.artorsr,i,l. Equationssatisfiedby the extremal g58/5g),285-2gl'MR 2l-928' [6',9' tior.s.Ann.Polon.Math. 5(l 17, 251 ' Bull' J. Remsrkson a classof analyticfunctions Zamorski, 1504. 8(1960)'277Phys' Acad.Polon.Sci.Ser.sci. Math. Astroncm' 24A-40' 12,6' 9' 380.(Russiansummary,unboundinserts)MR 1 6 ,t 7, 2 5 , 3 6 i for theextrpmalstarlikefunc1505. zarnorski,J. Differentinrequations 22A(l)-295-16, tions.Ann.polon. Mat1. itr960), 279-283.MR 9, 241 of thestarlike 1i06. Zamorskl,J. Theestimationof the third coefficient Math. 8(1960),185-191'MR function tryithc pole. Ann. Polon. 22A(2)-t377. [6, 9, 17,25, 361 schlichtfunctions.Ann. 1507. zartorski, J. About tie extremalspirci MR 24A-37. |6| Polon.Math. 9(|960/6|),265_273. belonging' . Zarnorski,j . Estimationof the coefficientsof furrctions 1.508 Prace Mat' to twc ,ior.r6 of k-sym,netricschtichtfunctions'

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of opial, Beesuckand Levinson' llz. Pederscr, R.N. on an ineauotity 1965'p' 174' t:591 Proc. A.M.S., voi i5, no' t' Ftb ' problemt oia coefficient regionsfor 113. Pfa-ltzgraff, J. A. Extremal by a Stielties integrol' Notices' analytic functions represenietl i s s u en o . 7 4 , A p r i l | 9 6 4 , p p . 3 6 3 A m e r . M a t h . S o c . ,v o l . l l , n o . 3 , 364. 129, 591 FoberschenForyiiome scnrichterFunk,4. pommerenke, ch. r-tberdie t i o n e n . M a t h . Z . 8 5 ( | 9 6 4 ) , | 9 7 . 2 0 8 . M R 2 9 _ | 1 2 9 . [ 5 3 j Funk' Familien onolytischer ,5. pommerenke, ch. Linea'r-invariante g@),108-154;ibid. 155(1964),226tionen I, II. Math. Ann. 155(t

262.MR 29-rr24.l44l

functionsand univarent power series ,6. pommerenke,ch. Lacunary 29-919't39l Mich. Math. J. 1l(1964),2lg-223'MR onolytic functions' Trans' ll7 . Pommerenke,Ch. On close-to-convex Amer.Math.Soc'114(196/l)'176-186'[3'4'5'6'9'10'12'15'17' 2 2 ,3 0 , 3 8 ,4 1 , 5 8, 6 2 , 6 4 1 Proc' Amer' Math' poole, J. T. A noteon iariotionalmethods' l18. Soc.no. 6, 15(l964)'929-932't24l functions. probtemsfor schricht 119. poole, J. T . coefficientextrernar NoticesAmer'Math'Soc"vol'12'no'5'issueno'83'August 1 9 6 5P, . 5 8 6 't 9 , 1 7 , 2 5 '5 4 1 of tevetlinesunderunivalentconlzo. popov,V. L Starlikentitoi arcs Jorma!mappings.SovietMath.,March-April1064,vol.5,no,2, pp. 510-513. [6, 9, l0l bkmsfor a class l2l.Privalov&,G'K';Saran'L'A'someextremalprot offunctionswhichisstar.shapedinthedirectionoftherealaxis. no' 4' 4l(1964)' (Russian)lzv. Vyss.Ucebn.Zaue* Matematika MR 29-461'[6, l5' 40' 63] 126-130. l,lyrent exponsnns' M. c . cn thepartis! sums-o!certain 122.R.eade, MR 29-260.19,20'431 colloq. Math. 1l(t96itu), 173-179. Publ' Math' univalence' 123.Reade,M. O . On O:go*oiicriterionfor 5' l0l 11(1964) , ig-ql' MR 30-417'14' Debrecen of thefunctionolIU@),"f(.,)' |24. Red,kov,M. |. Therangeof values Trudy Tomsk.Gos. , (a),1 , (0))in the rroris, ti .f@)| l. (Russian) f 59-68.MR 29-260'l29l Univ. Ser.Meh. -Mat. 169i1963), funco-fcertainimpedance 125.Reza,F. M. on the schtichtbehavior t i o n s . I R E T r a n s . C i r c u i t T h e o r y , C T - 9 ( 1 9 6 2 )with , 2 3 |positive _232.t28] probtemfor functions tz6. Robertsoil,M. s. ,4n extremat realparl.Notices,A.M.S.Vol.11,no.6,issueno.77,Oct.|964,

I-

110

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

p . 6 7 3u . , 2,4, 6, l0l ' and close-to-convexity 127. Robertson,M. s. Rsdii of starlikeness 847-852'12'4' 5' 6' li' 121 Proc.Amer.Math. Soc'16(1965)' I' II' Composito Potenzreihen' W. tlber beschriinkte 1 2 8 .Rogosinski, M a t h . 5 ( 1 9 3 7 ) , 6 7 - | 0 6 ; ( 1 9 3 8 ) , M 2 - 4 7 6 . 2co., b | | 7New - 2 6 9York' .||,22| chelseaPubl. series. Fourier w. Rogosinski, r29. 195b,176pP. MR ll-347 ' t59l conformede domaineslimit€s A. Sur la repr€seniation 1 3 0 .Rosenblat'-, l9t7 ' tl5 ' 22' 6ll sur le cercleclerayon u-n'Krak' Anz' l 3 l . Royster,w.c.APoissonintegralformulafortheellipseandsome [6' Amer.Math.Soc.no. 4, 15(1964),66|_670. apptications.Proc.

7 , 1 8 ,5 7 1 of rationa! 132.Rubinst ein, z. Extension of two resurtsin the theory Soc' ;f analyticfunctions' Amer' Math' functions to certain classes 73, Feb.1964 (Abstracll't59l Notices,vol. ll, no. z,issueno. polynomialsand their zeroes' 133. Rubinstern,z. some inequalitiesfor P r o c . A m e r . M a t h ' S o c ' , n o ' 1 ' 1 6 ( 1 9 6 5 ) ' 7 2 - ' 7 5 ' [ 4ot' 5most ] p in convexof order 134.Sakaguchi,K. Meromotrphicfunctions Natur' sci' l9(1961/62)' 109one direuion J. Nara catugBi univ' l l 2 . M R 2 7 - 3 1 3 .[ 1 0 , 1 4 ' 4 1 ] theorem for a certain cluss of 135. Sakaguchi, K. A repres;entition Japan 15(1963),202_209.MR mregularfunctions. J. Math. Soc. 2 7 - 3 1 3 [. 4 , 5 , 6 , 1 7, 2 3 1 Meromorphicfunctions rnultivalently 135. sakaguchi,K.; watanabe, S. Gakugei univ' Natur' Sci' starlike in o wide sense.J. Nara I l(1963), 3-7. MR 27-314' ll4' 231 von einer meromorphenFunk137. Sato, T . Ein Satz uber Schtichtheit Jap' l1(1935)' 212-213'ZlL 12-171'UOl ticn.Proc. Irnp. -a^cacl' oi order o' Amer' J' Math' 138. Schild, A. On starlike finctions 8 ? ( 1 9 6 .55) 5 - 7 0 . [ 6 , 1 1 , 1 5 , l 7 l oi posirivefunctions,Nctices,A'M'S'' w. J. Some notels 139. Schneicler, g3, Aulust 1965,p.586 (Abstract).[2j vol. 12, no.5, issueno. and non-'o*vex domains' J' Math' 140. sonc, N. univqlentfunctions S o c . J a p a n 1 5 ( 1 9 6 3 ) , 1 9 1 _ 2 0 | . M R 2 7 . 3 | 4 . | 4 , 5 , 1 6 univalenl ,17,38] teve! curvesfor properties of-su. 141. Stepanova,O. Y . Certain (N.S') 61 (103) (1963)' conformc! moppings. (Russian)tvtat. 24' 251 350-361.MR 27-313'[6, 7, l0' of iaber polynomials' (Russian) proprrties l4Z. Suetin, P. K. The basii lzs-t54. NIR 29-1129'[531 (li8),'convex uspehiMat. Nauk t9(1964),no.4 of functions' Noi'iuss' 143. suffndge, T. J. convolutions A.M.S.,vol.12,nc'2'issueno'80'February1965'P'244 (Abstract).[4, 5, 10, 47]

,&

APHY SUPPLEMENTARY BIBLIOGR

111

of convexfunctions' Notices' i44. Suffridge, T. J. convolutions Augus1965'pp' 579-580 A.M.S., vol. 12,no' 5' issueno' 83' (Abstract).[10' 47] Strgaku theoremof Jenkins'(Japanese) 145.Suita,N. O; thecoeff;cient I 2g-r37'MR 29-45' l24l 14(1962/63), a7 uitvarentfunctions reratedto 146.Suita, N. ,4 distortion theorem 26-30' Sem.Rep. 14(1962), symmeyicthree points.Kodai Math. MR 27-59.[9, 15,17,25, 58] tJnivairn.t *ippings of planedon:ainsend setsof l4j. Suvorov,G. D . measure,'ero' Dokl' Akad' prime endsoJ a domainof geniratizeC t49] MR' 27_73,|. Nauk SSSR|52(|963),296-298. theorems' Anrer' J' Math' vol' 148. Taam, choy-cak oscillation 317-324'I\{R 14-50't3U 74(195D, zeroesof functions of Sturml4g. Taam, Choy-tak on the complex 3(1953),837_843.MR Liouville type.Pacific J. Mathematics ' tn 15-625' [3 u theorems oJ ^ ^^ir ^ti nn n l 5 0 . T a a m , c t r o y . t a t < N o n . o s c i l t a t i o n e n c c o r 4 p a r |d^ Scoefficien o ts' Por-

comprex-varue rinear different i ar equat io ns wit h t u g a l i a e M a t h e r n a t i c a l 2 ( 1 9 5 3 ) , 5 7 - . 7 2 . M R 1 4of_ 8doublv 7 3 . [ 3con1] conJormalmapping ur:ir-ot€rtt on M. P. Tamrazov, 151. n e c t e d r e g i o n s . ( u k r a i n l a n . R u s s i a n a n d E n g l i s hMR s u m27-59' maries) 1962,ll42-1145' Dopovidi itaa. Nauk ukrain. RSR

t60l conforin thetheoryof univarent p. M. someestimates r5z. Tarnrazov, Russian (Ukrainian' mal mappingsof aoy,ily connectlddomains. Nauk ukrain' RsR 1963' andEnglishsum*urr.riDopovidiAkad. l 160-1163.MR 29-1125'[50] of a pottyntcof nf the thpderivative rler roots of the "^ 153. Walsh, J. L. On the locatiin InternationaldesMath6matinomisr.comptes Rendusdu congrds c i e u s . S t r a s b o u r 8 , 2 2 - 3 0 S e p t e m b r e 1 9 2 0 ' [ 5traiectories 9] of the of orthogonal curvature the on Note L. J. walsh, 154. 2' no' Amer' Math' Soc' level curvesof Green'sfunction III'Bull' . R 1-210't591 4 6 ( 1 9 4 0 )1, 0 1 - 1 0 8M of a o7 tie zeroesof the derivatives 155. Walsh, J. L. On the location polynomialsymmetricintheorigin.Bull.Amer.Math.Soc.No. 10, 54(1e48);942-s4s'MR 10-250' t59l of reiet curvesof Green'sfunction. 156. warsh, J. L . Noteon ,n' shape Anter.Math.Monthly,Dec.1953,67:r-674.MR15-4u.|59| of tevetcurvesof Green'sfunction' 157.Walsh, J. L. Noteoi"rt , shape 6 1 1 - 6 1 6M . R 1 5 - 3 1 0 '[ 5 9 ] D u k e M a r h . J . n o. 4 , 2 0 ( l 9 j : ) , of the ovals of lemniscates'Studies 15g. Walsh, J. L . On the coniexity topics' pp' 419-423'Stanford in mathematicalanalysisand related

II2

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

Univ. Press,Stanford,Calif., 1962-MR 27-317' U0' 491 159. Waszkiewicz,J. Sur certainsprobtdmesextr)moux dans la famille des fonctions univalentes born1es inf€rieurement dans le cercle no. 3, 30 pp. MR K(-, 1). Bull. Soc. Sci. LettresL6dr. 14(1963), 29-694.[9, 15, 58] ld0. Whiteley,J. N.,A/ofeson a theoremon convolutions.Proc. Amer. M a t h . S o c .n o . l , 1 6 ( 1 9 6 5 )l -, 7 . l 4 7 l 161. Widder, D. V. The Laplace Transform. Princeton Univ. Press, London, 1946,406PP. MR 3-232. t59l 162. Wigner, E. P. On the connectionbetweenthe distribution of poles an(i residuesfor on R function and its invariont derivative.Ann. of Nlath. (2) 55(1952) ,7-r8. MR 13-733.t46l Mathematics 163. Wilf, H. S. for the PhysicalSciences.John Wiley and Sons,Inc., New York , 1962.284 pp. [441 164. Wilf, H. S. Calculations relating to a coniecture of P6lya snd Schoenberg.Math.Comp. 17(1963),200-201.MR 28-798.[10' 47] 165. Wintner, A. A criterionfor non-oscillatorydifferential equations. 10-456' Quarterlyof Applied Mathematics,7(1949),115-117.MR

[3r]

of conjugatepoints. Amer. J. 166. Wintner,A. Crt the non-existence MR 13-37.t31l 358-380. Math.73(1951), d'une th1ordmede Schwarz.C. R. g1n1;"alisation 167. Wolff, J. Surune 926),500-502.146l Paris183(1 168. Zlotkiewicz,E. On o variationalformula for starlikefunctions. (Polish and Russiansummaries)Ann. univ. Mariae curie. 1 5 ( 1 9 6 1l )l l,- 1 1 3 . I v i R2 8 - 4 3 4 . 1 6 , 2 4 1 S k l o d o w s kSae c tA

pr'-

I\4ATHEMATICAL -IOURNALS

113

MATHEMATICAL JOURI\ALS

Following is a list of twenty-two mathematicaljournals and paperson refer to schlichtfunctionswhich they contain. Numberswithin brackets ((A" indicate t1e main bibliography; numbers precededby the letter referencesto the SupplementaryDibliography' Acta Mathemoiiro,vol. l-113 (1882-1965)[18, 293, 508, 632, 648, 692, 840, 895, 945, I I 88, 1441,14801. American Journal of Mathematics, vol. 22-86 (1900-1964)[595' 5 9 8 , 5 9 g ,9 6 6 ,g 7 0 , 9 7 5 , 9 8 0 ,1 0 8 5, 1 1 4 2 ,1 1 4 6 , 1 2 5 01, 2 5 3 , 1 2 5 41, 2 7 2 , , 1 4 8 ,A 1 6 6 1 . 1 3 3 0 ,1 4 9 2 A Annals of Mathematics,vol. 8-81 (1906-1965, series2) 152,59, 215, 224,360,364,452,456,457,545,593,603,609, 614,615, 616,621,633, 1147,ll4g, 1150,1153,1156,1207,1262,1327' 534, 944, 1060,ll*, 1373,1476,A162l. Archive for Rational Mechanics and Analysis, vol ' 1- 19

II4

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

(1957-1965) [205, 266,3M, 3461. 7-7 | Bultetin cf the American Mathematicol society, vol' ( 1 9 0 0 - 1 9 6t5o)t , s + ,8 8 ,1 6 6 ,1 g 1 , 2 7,72 7 8 ,3 3 3, 3 4 7, 4 2 9 , 4 4 65, 3 6 ,6 2 8 ' , 1 4'1 1 1 4 31' ,1 4 5 ' , , 1 4 01 6 3 5 ,7 5 0 ,8 6 9 ,8 7 7 , 8 7 gg, 7 l , g 7 7 , 1 0 5 21, 1 0 9 1 1 3 6 11 4 6 l ' 1 1 4,81 1 5 2 ,1 1 5 51, 1 6,8l l 7 l , l z 0 4 , 1 2 5 5 , 1 2 5 7 , 1 2 7193, 3 1 , ' 1 4 6 3A, 1 9 ,A 5 4 ,A 1 5 4 ,A 1 5 5 1 . [91, 169, vol. I -17(1949-1965) CanadianJournalof Mathemotics, 1 7 2M , , 6 2 6 , 1 1 5 81. 1 6,1l 2 l 4 l . [l 1, 90' 92, 103, . l-?2 (1935-1965) Journal,,u'ol DukeMathematical , 1 0 l,l 1 , 1 6 l , 2 | 9 , 2 4 8 , 3 0,13 2 0 , 3 2 9 , 3 3 6 , 3 5 8 , 3 8 0 , , 091 , 081 1041 , 0 51 1 1 2 0l'l 5 l ' 5 2 g , 5 3 16,M , 7 5 5 , 8 7 5g,0 4 , , 9 l l9, 6 4 , 9 6 8 , 9 8130, 3 41, 1 0 7 , 1243,1249, 1154,1159,1170, 1209,1210,1212,1223,1233,1234,1236, 1274-1362,1433,1473,A.9l, A92,Al57l. 1620,622, Illinois Journaloj Mathematics,vol. l-9 (1957-1965) 753,1478,A48,A611. Pureset Appliqu'es, vol' 2-44 (1923Journal de Mathematiques 1965)[366,941,1443]Mathematik(formerlycrelle "Iournslfilr die reineund angewandte 1424'1425'142'6],' [581,1038,1416, vol.122-217(1900-1965) Jorrrnal), qnd Apptications,vol' l-11 ,Iournal of MathematicalAnalysis ( 1 9 6 C - 1 9 6l M 5 )9 , l 2 8 l l . sociery,vol.l-40 (1926-1965) of Journal theLondonMathematiccl 519' g 5, 3, 1 6 ,3 2 5 , 3 2 6 , 3 3' 374 0 ' , 4 8 9 ' , [ 8 5 ,I 1 3 , 2 1 1 , 2 1 6 , 2 1 7 , ? , 2 8 ,32M 974',1035' 521,522,5g4,608,612,662,663,6&, i54,817, 865' 892' , A26,A33' A42,A51' 1041,1073,1089,1102,1103,1186,1323,1335 A 8 5 ,A 9 8 1 . 194,116, 123' Annalen,vol. 53-158(1900-1965) Mothematische , 0 9 '1 0 3 7 ' 1 7 3 , 1 7 4 , 1 8158, ,71 8 9 ,! g 1, ) 2 3 , 2 g 4 , 4 8 34, 8 7, 5 4 1 , 6 9 08, 8 2 9 1040,1M7,1059,1080,1088,1278,1333,1360,14441' 120,62, ll8, 162' zeitschrift,vol. 1-88(1930-1965) Mothematische 53',2' 486' 523',528', 45),485, 300,302,?03,-324,341,342, 153,274,280, 893',916',919', 549,666,659,693,694,8M,809,810,812,8M,845,881' 1 3 5 , 1 3 61, t 7 7 ,1 1 8 0l,l 8 i , 1 3 4 0 , '31 3 5 41' ' 3 5 9 ' 9 4 8 ,1 0 4 31, 0 7 11, 1 3 4 1 1417,1436,1438 , 1439,1467,A1141' 1233,255' vol. l-12 (1952-1965) of Matheniatics, Journat Michigan i012', 1070' 1068, 1067, 1066 9g4, , 629,656,657 ,859, 872,888,914, t 0 7 4 , 1 1 0 6l ,l , l 2 , 1 1 6 7A, l l , A 3 4 ,A 8 l , A 9 6 ,A l 1 6 , A 1 2 6 1 ' 3!5' Pacific Journa!of Mathematics,vol. l-14 (195l-1964) [279' 1300', 5 5 1 ,7 5 2 , E 7 6 , 9 1150, 6 3 , 1 0 7I61.0 4 ,I I 1 7 , 1 1 2 2 , 1 1 6 I21, 5 3' 1 2 6 9 ' 1 3 0 7A, l 4 9 J . vol' I-16 Proceedingsof the American Mathematicalsociety,

A

MATHEMATICAL JOURNALS

115

271'288',335',432',433'434',437', U57,160,17l,l81' 264', (i950-1965) M 3 , 4 9 2 , 5 0 9 , 5 3 0 , 5 5glz,gsr 2 , 5 5 3 , 5 8 0 , 5 g 6986', ' , 5 g1118' 7 ' , 6 1119', 0 1 ' , 6ll57 0 2 ' ', 6ltf!y''', 07',815',873',889' ' 984'985', g90,891, 913,gl'l,918, 1427 ', 1435', 1423', 1403' 1414', 1398', 1257,1276', 1175,12i1,1265,1266, All8' Al3ll' 1 + l t , ' , 4 7 2\,4 7 7 , 1 4 7 9A,3 o , society'vol' 1-54series2 of theLondonMathen;ot'ical Praceedings 495', 3 s ( 1 9 5 1 - 1 9 6 [53)3 4 ,3 3 8 ,3 3 9 , 4 9 0 ' ( 1 g 0 3 - l g 5 l xr i o r .i - r 5 , s e r i eg6i 1309',1325', ', 1248', 1075',1187',1247 4g7 ,5M, 512,665,846,862, ',

'"'9\nuarterlv.lournal oJtv\t!t".t:'.i::'":t:',-.to;liltlli"li33 ,i?tJJt 2 (1950(rqlo-1949);vol. l-16, oxtord series

vol. I -z0,oxfordseriesr 1965)tl95, 196,3l'l, 494,498,8631' vol. 1-6 (1900-i965)[81' 179'831' SovietMathernatics-Doktady, t l 1 4 ,A 1 2 0 1 . society,vol. l-l18 of the AmericanMathematicar Trsnsactions ( 1 9 0 0 - 1 9 6 5 ) u 0 , 8 9 , 9 3 , 2 ? ! ' 2 4 g ' 2 g g ' , 3 1610', 8 ' 3 56ll' 7 ' , 3613', 6 1 '617 4 2',8624', ',431',435',436' 606', 5g2',605; 57g' 438, 43g,440,411,445,451" g 7 3 ,g 7 g '1 0 1 3 i' 1 , 6 0 ' 1 1 6 5 1' ,1 5 '5, l l 7 2 ' 1 1 7 4 ' , 6 2 5 , 6 3 0E, l 4 , 8 7 8 ,8 8 7 , 1468' nzl' 1322'1332'1415' 1464'1466', 1280,1282:, 1206,1215,12',73, A52,A551. society,vol. 1-31' of the ArnericanNtathematicar Traitsrstions 426'826'828'A88]' [371' 3'73'375'376'423' 2 (1955-1963) series

5

116

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

EXPOSITORY PAPERS

Following is a list of publicaticns which are devotedwholly or in part to a general survey of the development of the theory of univalent and p-valent functions. Nunrbersin bracketsrefer to the main bibliography. Numbers precededby the ieiter "A" refer te the SupplementaryBibliography. An asteriskindicatesa particularly comprehensivesource. 1.239 (Chapter8); lj00 (pp. 198-212);86abp. 163-185,205-226\; 1 2 5( p p . 7 i - 8 3 ) ; 1 0 6 4( v o l . 2 , C h a p t e r2 1 ; 4 0 3 * ;l 3 3 l * ; 1 2 4 0 * ; l M ; 9 7 8( C h a p t e r5 ) ; t 2 4 l ; 1 2 6 ( C h a p t e r5 ) ; s 1 4 ;5 l i * ; 6 1 8 * ; 5 3 7 (vol. 2, Chapters17, l8); 1305 4ll; 886; 939; A24; A5l; Al15; Ai63 (Chapter6)l

TOPIC REFERENCES

II1

TOPIC REFERENCES

closely topics dearing directly with or Following is a list of sixty-eight p-valent functions. Following each relatedto the thecry cf univJint urro resurtspertainingto that topic' topic is a list of referenceswhich contain numbcrs refer to the rnain bibliography; Numbers v,,ithin brackets (. A' ' refer to the SupprementaryBibriography' The precededby the letter . . . , T68 for purposesof referencc' topics are numberedTl, T2, ff, a containsso many referencesthat Topic Tl5 (Distortion Theorems) T65' T64' T56, T58' T61'-T63' breakdownof T15 is given iV fopics of ropic T17 (coefficient T66, T67 and T6g. Similarlvi u bieakdown T54' T36, T38, T50, T51, T52' and Bounds)is givenby T21,Ti5"T30, conT44 (Sur'ey Articles) should be The referencesgiven under iopi. the other topics. sulted in connectio' with any of

hr--

118

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

T l . The Principle of Subordination. u , 35, 43,87, 100,102, 111, 130,132, 134,139,140, 212,231,320, 3 6 7 ,3 8 2 ,3 9 2 ,4 1 4 ,4 1 7 ,4 2 0 ,M 3 , M 6 , 5 0 3 ,5 9 8 ,6 0 5 ,6 l l , 6 7 7 , 6 8 5 , , &, 7 4 3 , 8 0 2 8, 3 6 ,8 3 8 ,8 5 5 ,8 5 6 ,8 6 3 ,8 7 0 ,8 8 7 ,9 1 0 ,9 5 3 ,9 5 6 , 9 6 0 9 9 6 7 , 1 0 6 8 ,1 0 7 1 ,1 0 7 2 ,1 0 8 8 ,l l l 7 , 1 1 4 4 ,1 1 6 3 ,1 1 6 5 ,1 1 7 4 ,1 1 7 9 , l l 8 l , 1 1 8 5 ,1 1 8 6 ,1 1 8 7 ,l 2 M , 1 2 7 8 ,1 2 9 0 ,1 2 9 1 ,1 2 9 3 ,1 3 1 9 ,1 3 4 1 , , 14, A15, A126, Al28l 1 3 6 6 , 1 3 8 2 , 1 4 7 71,4 8 0 ,1 4 9 4 A -F^

Lt.

Functians af Posiiive Real Part. 14,34, 46, 60, 108,186,196,226,233,268,272,315,350,380, 412, 426,456,519, 526,528,530, 577,703,7 17,7 18,7 19,720,721,887, , 8 8 ,9 9 6 ,1 0 0 0 ,1 0 4 1 ,1 0 9 9 ,1 1 0 5 , 8 8 9 ,8 9 0 ,8 9 1 ,9 1 3 ,9 6 8 ,9 7 4 , 9 8 5 9 1 1 4 0 ,1 1 4 2 ,1 1 4 4 ,1 1 4 7 ,1 1 5 1 ,1 1 5 4 ,1 1 6 6 ,1 1 6 7 , 1 1 7 71, 1 7 8 ,1 1 8 0 , 1 1 8 1 ,1 1 8 7 , l 4 M , 1 4 1 7 ,1 4 7 7 , , 1 2 1 3 ,1 2 7 8 ,1 3 2 0 ,1 3 4 0 ,1 3 6 1 ,1 4 0 1 , 5161 , 5 1 8 , 1 5 2 4A,l , A 3 1 , A 3 3 , A 7 l , A 7 2 , A 7 3 ,A 7 8 , 1 / 8 5 ,1 5 0 4 1 A91, A92, A94, A126, Al27, Al39l

T 3 . Integral Means. 1 7 9 8 6 , 8 8 , 1 3 5 ,1 3 9 ,1 4 5 ,1 4 7 , 1 4 8 ,1 5 2 ,l E l , 1 8 4 ,1 9 6 , 2 3 0 , 2 9 4 30rJ,305,328,337,338,339,378,407,409,410,413,417,423,489, 4 9 0 ,4 9 5 ,4 9 8 ,5 1l , 5 1 9 ,7 4 7 ,7 4 8 ,7 4 9 ,7 ) 2 , 8 3 1 ,8 3 2 ,8 3 3 ,8 3 4 ,8 3 5 , 8 4 6 , 8 6 2 , 8 9 4 ,9 0 1 , 9 5 2 , 9 5 3 , 9 5 4 , 1 0 6 9 ,1 0 7 1 ,1 0 7 2 ,1 0 8 2 ,l l l 7 , 1 1 1 8 ,1 1 4 3 ,l l 4 r ' , 1 1 4 6 ,1 1 5 0 ,1 1 5 1 , 1 1 7 1 ,1 1 8 6 ,1 1 8 7 ,1 2 7 8 ,1 2 8 0 ' 1300,1322,1323,1325,1335,1338,1356,1391, 1425,1471,477, A1171 T4. Sufficient Conditions fcr Uuivalency (p-valency). 1 2 2 ,2 3 , 2 4 , 2 5 , 2 6 , 5 2 ,7 7 , 1 0 8 ,i 2 l , 1 5 1 ,l 7 l , 1 7 2 ,1 7 5 ,1 7 6 ,1 7 9 , 18C,I 82, 183,205, 2ll, 217,227,211,255,259,289,295,296,297' 3 2 7 ,J 3 5 , 3 3 6 , 3 5 0 ,3 5 4 , 4 2 1 , 4 2 4+, 2 8 , 4 3 74, 8 5 , 4 9 2 , 4 9 3 , 5 0 05,3 0 , 5 4 2 ,5 5 4 ,6 5 2 , 6 5 56, 5 6 ,6 6 8 ,6 7 2 ,6 7 4 , 6 8 7, 7 1 9 , 7 4 3 , 7 4 6 , 8 4 88, 5 0 , 38 , 7 ,8 9 0 ,8 9 1 ,9 1 1 ,9 1 2 , 9 1 7 , 9 1 89,2 5 , 9 4 0 , 8 5 9 ,8 7 4 , 8 7 6 , 8 7 7 , 8 8 8 9 6 3 , 9 7 1 , 9 8 1 9, 8 2 ,9 8 4 , 9 9 7 ,1 0 0 1 ,1 0 0 6 ,1 0 0 7 ,1 0 1 0 ,1 0 1 1 ,1 0 1 9 ' 1020, 1021,1023,1025,1027.1029,1036,1058,1063,1071,10'72, 1 0 9 0 ,1 0 9 4 ,1 0 9 5 ,1 1 0 5 ,1 1 0 6 ,1 1 0 7 ,1 1 0 8 ,l l l 0 , 1 1 1 1 ,1 1 1 2 ,l l i , . 4 , l l # , i 1 4 5 , 1 1 5 6 ,1 1 6 0 ,1 1 6 2 ,1 1 6 6 ,1 1 7 6 ,1 2 1 8 ,1 2 2 0 ,1 2 2 2 ,1 2 3 1 , 1266,1267, 1273,t286, 1301,1310, l3l7 , 1337,1338, 1362,1365' i367, 1371,1372,1398,1399, 1412,1428,1429,1432,1434,1435, 1485, l4gl, 149't,1508,1509,l.slO, 1519, 152A,1522,1523,Al0,

TOPIC REFERENCES

119

A30,A35,A31A38,A80'A81',A90'A91',A93',A100',A117' A140',A1431 A12l Al ze, ttz7, A133'A135', (and generalizations)' T5. Ciose-toConvexFunciicns 11 | 28,9 7 ' 8 9 8 ' 9 2 2 ' 1 1 2 9 , 2 8 2 , b 5 6 , 6 8 7 , 7 6 5 ' 17 16 06 5' 81, 5110'681,5140' 8715, 19 0' 8881, 71'1809|,6 1 0 0 51, 0 0 71, 0 7| , | 0 7 2 ,| 0 7 5 , 1131,1132-1218,1352,1435'15]-0',1520'1522',t523',A33',A78' A9l,Ag2,A93,Al04,A117'A123',A127',A135',A140',A1431 generalizations)' T6. StarlikeFunctions(and 92',97',98', 52' 55' 60'-7.1',80',8l' 82'-8]',90', 34, 32, l' 3 28,30, 23, 14, 99,108,109,111,119,'128''tlz'134'137',142',156',157'216'21'l' 235,242,243,247,255,258'260',261^',274',282',257'',301',336',352', 430',43r',433',43'!'437'442'4r'5', 426'', 4l'7,izz' 4C0, 385, 381, 353, 673' 659'66r'663'665'

481,500,5i9,55r,ssz',s;,;sr{, 91?:,6s3, 846'853',856' 731', 733', 1??',723', lg', 1 16" 8"1 67 67'1, 6, 6'.7 5, 6i 4, 67 932',934',952', 909',gl7',91-8',

9O8; 888,889,890,891,895, 89;'898;ggg:1000', 1004'1005' 1001',J003' gge'998', 953,956,985,986,990; 1 0 2 1 , 1 0 2 2 , 1 0 3 8 , 1 0 4 2 , 1 0 6 3 ' 1 0 1 : ^I 1 - '0, 170'1,' 1 7 02'8',,11102743l' l',,4120' 7 5 ' , 1 0 ? 6 " ' 0 7 9 ' , 0 9 ; ;1 0 9 5 r' r 9 l ' , i 1 0 6 ' 1 0 8 3 1, 0 9 01, 0 9 1 1 1 1 6 41' ,1 6 6 1' ,1 6 71' ,1 7 5 ' , 1 ,1 5 41, 1 5 61; 1 5 91; 1 6 91' 1 6 3 ' , 1144,1153 1 1 8 7 , 1 2 0 9 , | 2 | 2 , | 2 | 4 , , | 2 | 5 . , | 2 | 7 , | 21360', | 8 , 1 2 1 9 , | 2 2 1 , | 2 3 1',l , | 2 6 5 , 1352',', 1365'1366'1367 1319', 1339' 1311" 1278, , 1266,1267 1 3 7 0 , 1 3 7 4 , 1 3 9 8 , 1 4 1 4 ' 1 4 2 6 ' t 4 2 7 ' 114520 961 ',,5104731,75' ,11841,3581' 9 , 1' m 0 ' , 1 4 / l l 9 ' , 1505' t s o + , r s o l , 1 5 0 i , t 4 g g , t4g4, 1495, A35' A37'A38' A45', A26',A3'2', 1524,A2, A4,All, iiz' eis ' A98',A102', A86', l 2 l ' A87',491', A92',-A93', A l 3 5 ' A41A48,A71, A78,-Ati'' A , 13l' A133, A 1 2 6 'A 1 2 7A A 1 0 4 ,A 1 0 6A 1 1 7 ,A i 2 0 , A 1 3 8 ,A 1 4 1 ,A 1 6 8 l

InvolvingArc-Length' T7. Relations 720' [ 2 , 8 0 , 8 1 , 8 2 , 8 6 , 8 8 ' 1 4 5 eoie', ' 1 5 2 ' 1 9 4664', ' 2 g665',700' 4'3N:37 4 17'718' 1'346'3 50'366' -;02'oiz' en' 545,610, 9Ui', 444,519, ', 1072'1073',1075' ',796, 909',g32',i062',1071 B2O'887, 767 , ' ,l l ' , ' , 5 1 7A 1 4 1 01 ' , 4 3 5 1' ,4 8 7 1 , 1 4 ,61 2 3 0 ' t 2 5 3 ' 1 1 j 4 7 ' , 1 1 3 01 , 1 4 31 A131',Al4U A25,A33, A40, A88' Ag4'A96', I - la" ll' T8. Boundsfo, l\on+t A94] 521'1075',1368', [56, I 46, 149,l5A,24l'

r20

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

T9. Meromorphicunivalent(p-valent)Functions. ' 09' 1 4 ! ,1 5 5 ,1 7 6 '1 8 3 2 [ 3 , 5 , 3 6 ,7 3 ,7 4 , 7 5 , 7 6 , 8 18, 2 , 1 1 6 ,I 1 7 , 372, 368, 363,364, 2|5, 2|6, 234,235,264,277,230,285,307,335, 4 1 8 '4 2 6 ' 3 8 1 ,3 8 3 ,3 8 7 ,3 9 0 ,3 g 3 , 3 9 53, 9 7, 4 0 0 ,4 0 4 ,4 0 7, 4 0 8 ,4 1 6 ' 595',601', 579; 482,485,492,507,508,54y', 434,436,452,455,481, 625,629,682,697,705,709,7|2, 7|5, 72|, 722,73|, 6|9, 623,624., 80 04 7 ,,8 5 9 ,8 6 6 ,8 8 1 ,8 8 8 ,9 2 1 ' 9 2 4 ' , 9 2 5 ' , 732,734,741,7R2,7g1,8 1020,1071,1072,1076' g7g,983, 935,986,987,996,1009, 951,971, , 1 2 8l,L & , i i 6 6 , 1 1 6 71, 1 7 6l,l i g , l l 8 4 ' 1 0 7 81, 0 8 31, 1 1 31, 1 2 5 1 1255' 1189,1214,1215,l2lg, 1228,1246,1249,1250,1253,1254, 1 1 3 3 3 , 390, 1 3 3 2 , 1 ,3 0 4 1, 3 0 6 1, 3 1 3 i,3 1 6 , 1 2 5 9t,2 8 3 ,1 3 0 2 , 1 3 0 3 1490, 1392,1397,1414,1416,1434,1451,1452,1459,1476,1481, 1518' ' l 5 l 7 1 5 1 4 , l 4 g l , 1 4 9 9 , 1 5 0 2 , 1 5 0135,0 41, 5 0 51, 5 0 61, 5 1 3 , A4, A30,A35,A50,A59,A60, A62,A89, A92,A101,A106'A107', , 1 2 2 ,A 1 4 64, 1 5 9 1 A 1 1 7 ,A 1 1 9 ,A 1 2 0 A (andgeneralizations) T10. ConvexFunctio,,ns 8 2 ,8 7 ,9 0 , 1 0 8 '1 0 9 '1 1 1 ' 1 2 , 4 , 2 3 , 2 8 , 2 9 , 3 1 , 3 4 , 5 2 , 68 30 ,,8 1 , 262,274, 295,296, l 18, 132,|34, |42, l 89,2|7, 243,247,255,,261r, , 3 3 ,4 3 7 ' , 8 3 ,4 1 2 ,4 3 0 ,4 3 1 4 3 0 1 ,3 3 5 ;n 6 : , 3 3 g3, 3 g J, 4 g , 3 5 53,9 1 3 660' M3, 4/t5,453,454,4g2,546,550,552,564,570,636,642,659, 73l-, 7 )5, 723, 722, 7 |9, 66!, 663,673,674,675, 676,677,703,7|6, 8 , 90, 91' , 8 7 ,8 8 8 ,8 8 9 8 7 5 : ^ , 7 6 : r , 7 6 2 ,,786476 , 8 5 98, 7 0 ,8 8 1 ,8 8 4 8 , lo32' 956.953,988,997,1cc5 909,g4l, g52,953, 896,8g7,898, 1091' 1 0 3 31, 0 3,71 0 4 2 , 1 0 6 31,0 7 01, 0 7,11 0 7 3 ,1 0 8 31, 0 8 81, 0 9 0 , 1 0 9 51, 1 0 11, 1 0,7l l 2 g , 1 1 4 2 ,l l 4 r ' ' , l 1 6 01, 1 6 31, 1 6 61, 1 8 7 , 1 2 0 9 ' , 1299' 1217,!21g, 1222,12-2g,1231,1265,1267,1278,1289,1292, 1438' 13t7,I 340,I 341,I 365, 1366,I 3?0,1412,1429,1434,\437, 1524', 1523, 1459,1477,148l, 1494,1515,1517, 1518,1519,1520, A93' Al, Al 5, A26,A35,A3?,A38, A65, A67' A71,A9l ' A92' A134', A126' Ag4,A95, A98, A107,A108,A117,A120,Al23' A137A , 1 4 1 ,A 1 4 3, A l M , A 1 5 8 ,A 1 6 4 l Tl I . RaCiiof Starlikeness. 368,369,381'396'48i.'500'502'673'675' [28,i 73,'ti4,742,243. 889,890,891,89?'908'909',914', 676,677,682,747,748,74g,854, 1370, 915,g,28,g34,g75,ggg,|042,1090,L2|7,|2|9, |267,|367, A l 3 8 i , 4 8 ,4 6 3 , A 7 7 ,A 9 4 ,A 1 0 4 ,A l z T ' i 3 9 S ,A 3 2 , A 4 1A T12. Radii of ConvexitY.

."d

TOPIC REFERENCES

I2I

128,29,31,173,174,241368,502,673,676,677,747'765',848', , 8 9 ,8 9 0 ,8 9 1 ,8 9 7 , 9 | 4 , 9 1 59,2 8 , 9 5 2 , 9 7 0 , 9 7 5 , 9 8 9 , 8 4 g , 8 5 08,8 7 8 g g 7 , 1 0 0 61,0 9 0 ,l c g z ,l l 3 l , 1 1 6 6 ,1 1 6 7 , 1 2 1 7 , 1 2 1 9 , 1 212296, 5 , Aii7. | 2 6 6 ,| 3 7 0 ,| 3 7 5 ,| 4 2 8 , A 3 2 ,A 4 7 ,A 9 1 r ,A 9 2 ,A 9 4 ,A 1 0 4 , Ar27l Functions T13. TypicallY-Real 1 6 8 |,6 9 , 1 7 03. 3 5 , 3 - | 2 , [ 4 ,5 , 4 6 . 5 55, 7 ,5 8 ,6 0 ,1 0 9 l, l 1 , 1 3 | ,| 6 ' 1 , 416.422,426,427,432,436,445,580, 607,526,629' 371, 375, 41,3, 7 L 5 .7 5 : ^ , 8 M8, 5 8 ,9 0 1 ,9 1 3 ,9 5 3 ,9 9 5 ,| 0 2 2 ,1 0 3t , 1 0 5 3 1, 1 2 0 , 1 1 2 11 1 4 0 ,1 1 4 2l,l # ' , l l 4 7, 1 1 4 91, 1 5 2I, i 5 5 , 1 1 5 6I, t 5 7 ,I 1 5 8 , 1159,1160,||62,1|77,1i80,|2t2,i337,|427,|43|,|476,A|, A7, A4l, A68, A73,A87,A9ll T 14. p-valentFunctions [ 3 , 3 6 , 4 5 , 4 8 , 8 9 , 9 0 , 9 2 , 1 3 5 , 1 3 5 , 1 4 0 , 1 4 1 , | M ' 1 4 6 '3 157'197', , 48, 53, 2 0 8 ,2 4 2 , 2 4 6 , 2 5 5 , 2 5 8 , 2 6 | , 2 8 2 , 32 08 58 ,,3 2 5 , 3 3 03,3 6 3 428,430,43|,438, 3E9,396,406,410, 373,376,388, 356,367,368, 678,679, 507,508,5|2, 574,575, 576,6|4, 644,668, 44I, 445,505, 8 7 7 6 8 0 ,6 8 1 ,6 8 2 , 6 8 36,8 4 ,6 8 5 ,6 9 8 ,7 3 7, 7 5 9 , 7 6 0 , 8 1 6 , , 8 7 9 , 9 2 3 , g25,94]^,g42,,955, 1001'1003,1004,1006,1019,1020,|02|, |022, 1159, 1 0 2 3 , 1 0 2 4 , 1 016190, 11, 1 4 81, 1 5 01, 1 5 11, 1 5 31, 1 5 41, 1 5 8 , 1428, 1210,1215,l2lg, 1220,1221,1231,1250,t371,1372,1427, Al36l Al34' 1429,1434,1435,l49g' 1500,A37,A38,A45, T 15. Distortion Theorems , 8 , 4 9 ,6 1 ,& , 6 5 , 6 8 , 7 0 , 7 1 , 7 2 , 7 6 , 9121' 8 l' 2 l ' [ 4 ,5 , 3 9 , 4 0 ,4 1 4 , 5 6 |, 5 7 , 1 7 0l,9 ! . ,| 9 7 , 2 0 9 , 2 3 1 , 2 3 4 , 2 4 2 , l 3 l , | 4 | , | 4 2 , 1 4 8 1, 5 5 1 28]l,282,306, 246,247 , 255, 256,257, 258,25g,260,261,262,263, ' , 8 7' , ' ' 8 5 3' 8 6 3 3 2 5 , 3 5 3 ; 3 5 5 , 3 35 6 6, , 3 6 7 , 3 6 9 , 3 7 5 , 3 7 6 ,3388313 4a4,407 ,408,412, 396,397 ,399,400, 3gg,3gg;3g0,3g2,3g4,3g5, 455', 413,4r5,416,418,42'6,427,431,,434,435,436,453'454', 557 5M, 532, ,558, 505,507,519, 474,481,482,484,500, 460,46:^, 627, 626, 62|, 599,605, 595, 591, 590, 559,560,570,573,577,585, 709', 698', 697 687' 684, ' 677 ,679,680,682,683, 641,644,659,661, 7 6l' 7 7 lL,7n:, 7rc:,7 23,7 24,7 25,7 33,737,7 42,749,758'759' 60' 833'834'835',846', 808,826,828, 7g3,804, 762,763,764,766,788, gg0, g5g,g67,970, 881,882,884,887,892,896, g4g,g50;g52,g53, 953,959,963,965' 908,909,916,921,932,g4O,943,951, 8g7,906; 1071', 989,1006,1008,1030,t032,lM3, 1048,1051,1053,1057,

-

I22

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

1072,1073,1076,1083,1095 , 1097,1098,I l0l , 1102,1103,I108, 51 05 , 11, 1 5 4 , 1 1 4 3 , l l 4 / ,1 1 4 61, 1 4 7 , 1 1 4 9 , 1 1 1 1 1 3 1 , 1 1 2 01, 1 2 5 , 1 ,1 8 91, l 9 l, 1 2 1 9 , 1 2 2 2l ,z M , 1 2 5 5 , 1 2 6 61 ,2 6 7 , 1 1 7 21, 1 7 3 , 1 1 7 5 1 2 8 01, 2 8,81 2 9 9 , 1 3 0 81,3 1 31, 3 1 61, 3 2 0 , 1 3 2 7 , 1 3 31 23 ,3 31, 3 4 0 , 69 , 7 ,1 4 1 6 1, 4 2 5 , 1 3 4 71, 3 4 8 , 1 3 7 4 , 1 3 7153,9 01, 3 9 2 , 1 3 9 5 , 1 3 9t 3 1499, r4r'/J,1456,1463,1481,1494,1496, 1426,1427,1435,1439, A 3 8 , A4l, 75 , , A 6 , A 2 5 ,A 3 l , A 3 5 , A 3 7 , 1 5 0 01, 5 1 01, 5 1 3 , 1 5 1A , 1 3 8 ,A 1 4 6 , A 6 5 , A 6 7 ,A 7 l , A 7 8 , A 7 9 ,A 9 4 ,A 1 1 7 ,A l 2 l , A 1 3 0A Ai59j Problems,OpenQuestions. Tlb. Conjecttlres, , ,333' 1 3 , 2 4l,l 0 , 1 3 8 ,1 4 6 ,l 5 l , 1 5 2 ,1 6 l , 1 7 2 ,1 8 4 , 2 7 8 , 3 031M 467, 512, 5I 6' 441, 445, 438, 432, 428, 431, 392, 339,346,360,364, 5I 8, 5I 9, 523,595,598,614,629,639,640,642,643,645,673, 674, , 51, , 3 4 ,8 3 5 ,8 4 9 8 , 6 7 , 7 8 17, 9 1 ,8 1 2 8 , 4 97 , 367 6825 , 8 47, 1 4 ,7 1 3 7 1055, 1063, 986,1035, 855,863,869,903,906,934,946,952,984, 1 1 8 6 , l z l D1, 2 1 4 , 1 3 0 16 3, 1 2 , 1 1 6 7 1 , 1 6 9 , 1 l 4 l 1131, ,11M,1159, 1346,1390,1410,1412,1425,1426, 1327,1329,1332, 1325,1326, 1433,1477,1490,1504,l5l5 , 1522,A7 , A25, A32,A33, A80, A106,Al40i Tl7 . CoefficientBounds [ 3 , 5, 3 2 , 3 7 ,4 5 ,4 8 , 5 5 5, 6 ,6 7 , 6 9 , 7 0 , 7 2 , 7 59, 2 ,i 0 3 , 1 0 7 ,l l 7 , , 0 5 , 2 0 6 , 2 0 i , 2 0281, 5 , 2 1 6 , 1 2 3 , 1 3 51,3 8 , 1 4 71,5 0 ,1 7 0 , 1 8 41,9 4 2 217,226,235,241,242,255, 256,257,259,261,263,264,269,27l, 271,294,304,305,328,329,349,355,363,364,365,370,372,374, 375, 376, 37g, 388,389,393.J94,396,407,408,dog,412,413,421, 428,430,431,432,415,436,M5, 493,505,509,5I 1, 512,5I 9, 521, , 8 6 ,5 8 7 5 , 01' , 996 5 5 2 , 5 5 4 , 5 6 2 , 5 6566,7 , 5 6 85,7 6 , 5 7 7 , 5 8508, 3 5 605,6I 0, tiI 9, 623,624,625,529,638, 639,640,645,65I . 651,660, 686,68'/,7C5,709,7 14,715,727,728, 661,677,679,682,684,685, , 9 5 , 8 M ,8 1 2 , 8 3 3 ' , 4 97, 5 5 , 7 8 87, 8 9 , 7 9 07,9 3 7 , 417 , 427 7377 , 407 868,870,882,883' 866, 865, 863, 859, 834,835,842,843,844,846, 983,984, 901,906,w7,924,925,957,958, 884,887,888,892,898, 1022, 1020, 1019, 1018, 1009, 996, 995, 985,986,987,989,990, 1030,1038,1069,l07l ,1072,1073,i075,1076,l08l' lo'23,1a24, 1 0 9 7 , 1 0 9l8l 0, l , 1 1 0 51, 1 0 61, 1 0 71, 1 0 8l,l 2 9 , l 1 3 l , 1 1 3 2 ,l l 4 0 ' ' , 1 4 61, 1 4 71, 1 4 8 , 1 1 4 9 , 1 1 5l 105, l, 1 1 5 2 , I l 4 l , 1 1 4 2 ,1 1 4 3 , l l 4 y 1 1 1 1 5 9 , 1 8 61, 1 8 7 ,1 1 8 91, 1 9 0 ,1 1 9 21,1 9 3, 1 1 9 4 , 1 1 5 8 , 1 1 5 41, 1 5 5 , 1213,1214, 1201,12A3,l2l2, 1195,1196,1197,1198,1199,120C,,

!l

TOPIC REFERENCES

123

lzw, 1246,1249,1250,1259,1267, 1215,l2lg, 1222,1233,123^., | 3 2 9 ,| 3 3 2 , | 2 8 4 ,| 2 g 3 ,| 2 9 6 , 1 3 0 81,3 0,9! 3 | 7 , | 3 2 2 ,\ 3 2 5 ,| 3 2 7 , , 7 7 ,l 3 8 l ' 1 3 8 21' 3 9 2 ' 1 3 3 31, 3 3 g1, 3 4 0 ;r 3 4 g , 1 3 6, 1g3 7 4 , 1 3 7 5t 3 1 4 3 5l'M 8 ' i 3 9 4 ,1 3 9,5 i 4 l z ' .l 4 ' / 5 , 1 4 2 6 , 1 4 2 17 4, 3 01, 4 3 11, 4 3'3 i499, | 4 4 9 , 1 4 5 01,4 5,1| 4 5 2 ,| 4 5 3 ,1 4 5 4 , 1 4,5|54 6 3 ,| 4 7 9 , 1 4 9 0 , A58', 1504,1506,1509,1513,1514,A4,A7' A25'A46', 1502,1503, A65,A86,Ag2,Ag4,Al0l,A106,A11i'A117'A119',A135' A 1 3 8 ,A 1 4 0 ,A 1 4 6 1 T18. RelaiionsinvolvingArea' 23L, 236,237, 250,277, 285, 350, 12,75,97, 137, 152,184,217' 7 2 0 , 7 5 87, 6 7 ,8 8 7 ' 417,429,435, 444,452, 496,6 8 7 ,7 1 7 . 7 1 8 , 1463,1487,A5, A6, l 0 ? 3, 1 0 7 6 ,l l l 7 , 1 1 8 9 ,1 2 8 0 '1324,1325, A l l , A 3 3, A 9 4 ,A 9 6 ,A l 3 l l T19. CoveringTheorems'

[ 3 , 1 0 , 2 0 , 3 9 , 5 3 , 7 3 , 7 4 , 7 5 , 7 9 , 9 7 , 9 8 , 9 92'3140' 0 1 '0,'3 ' l0 l 67' 1 2 0 ' , , 2' 17 00 1 ' 2' 1 71 , 9 32' 1 8 ' 1 2 2 , 1 2 4 , 1 3 7 , 1 3 g , 114401, , 1 5 81,8 4 1 309,310,348,360,384,3gr,3g3,4M,406'429'M4',4y';6',452',468', 598',614',621', 550', 524'538' 507,509, 493,505, 470,471,479,488, 6 2 7 , 6 4 2 , 6 4 7 , 6 8 5 , 7 0 5 , 7 0 9 , 7 6 1 , 7 6 2 , 7 5 8 ' 7 ' . 7 2 ' , 7893' 74',801',8M',8C7' 887',892', 881', 877 868' ', 852,853, 849, 846, 822,830, 810,813, 9 1 6 , g 3 3 , g 3 7 ' g 4 g , 9 5 1 , 9 6 1 , 9 6 4 , 9 6 7 ' 9 8 4 ' 1 0 1 1 ' 1102?1' ,04,' , 1 0 8 5 ' , 1 1 1 9 ' 1 1 8 71, 1 8 9 , | | 2 3 , 1 1 2 81, 1 5 41, 1 6 81, 1 7 c|,| 7 g , 1 1 8 41, 1 8 6 , 1319', 1289'l2g2' 1293'1295', 1277,1276;,1280, 1216,1265,1266, 1421', ' l4l8' 1419',1420', 1340;1358 ,1402, 1407 1324,1326,1327, A25' 1515' 1483' 1423,1424,1437,l#,g:,1462,1463,1467,1474, A36,A39,A83,A86,A91,Ag4,A95,A98'A99',A1021 T20. Partisl Sums,CesdroSums' 1 2 5 , 1 1 1 , 2 7 4 , 2 g 3 , 2 g 5 , 2 9 6 , 3 0 1 , 3 5 0 ' 355915''63, 357'4,6' 43182'6,'4513'2, ' 5 5 7 ' , 5 5 8 ' 5 5 9 , 5 6 0 , 5 6 1 , 5 6 4 , 556657, , 5 6 85,7 0 , 5 7 2 ' 5 7 5 ' , 6 5 3 , 6 7 2 , 6 7 3 , 6 7 5 , 6 7 6 , 6 7 7 , 7 3 3 , 7 g 1 ' 8 8 3 ' 8 8 7 ' , 9 2| |27' 7 , 9, 5 4 ' , 9 9 8 ' , 1 1 5 6|,| 6 2 , 1 0 0 51, 0 9 51, 0 9 91, 1 0 4r,r r : , | | 4 4 , 1 1 4 51, 1 5 3 , ' 3 6 11, 3 6,5| 3 6 7 ,1 3 7 01, 3 8'9| 4 7 9 , 1 1 9,1| 2 | 7 , | 2 | g , i 3 t z , t 3 6 0 1 t495, Al22l Resl Part' T2l. coefficientBoundsfor Functionsof Positive 1226,412,519,887,985,1144,1147'1151'1154',A3U

t24

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

T22. BoundedFunctions' [38,39,78,79,116,173,174'191',193',1g4',198',201',203',2m', 242,254,255,261,272,2g0'2g3'3?|7',330',369',378',379',396'412' ' 88' 5865 ' 875 : q3l ' 4 5 2 , 4 g 2 , 5 0551,9 ,f i z : , 5 3 85; 4 3 , 5 1 3 , 5 7 4 , 5 8 743',758', 662',664',665'700', 3; 62'7'639'641-', 589,590,591, 612,61 7',879', 8',7 867', 821',826',869', 7 7 59,7 60,7 61,'t62,',|68"7 69'77 L','T', gg'l 1009', 1049'1051' g25,g37,965, 96'7,g'72,n;'g77'g7g',988', ', , 2 0 '1, 1 2 2 ' , 1 1 0 31' ,1 1 51' 1 1 6I' 1 1 0 6 11 0 7 ,31 0 9 1 1 0 9 81; 0 9 91' 1 0 ? ' 1 2 0 51, 2 1 01, 2 2 1 , 1191 l l w , 1 1 7 2 , 1 1,7l l3g 2 " i r s + , 1 1 8 6 , , 1 2 0 ! ' | 2 2 9 , 1 2 3 0 , | 2 3 4 , | 2 , | 8 , , 1 2 8 0 , | 2 g 5 -1, 31 7390,71,31831003' 98, 3 11'331900, |' 3 | 2 , 1 3 1 3 ' , 3 4 g1; 3 6,11 3 7 7 '1 3 7 '8 1 3 1 5l,3 l g , t 3 4 3 1 Al', A23',A25', 1516',1519', 1439,1455,1456,148;, Ui8:7'1482', A26,A33,A58,A59,-A60'A70'A73',A117',A128',A1301 T23.RepresentationTheorems,structuralFormulas. 1 2 4 , 2 5 , 4 6 , 6 0 , 9 2 , 1 7 0 , 2 5 6 , 2 5 7 , 2 1 8659',6-60', ' , 2 6 2 ' , 665', 3 1 7686', ' , 3 1703' 9'353'355',3',72' 577'626-'65I', 4lg,422,426,436,5lt,540' 1073' 889',896',897',899',995', ii6,723,858,869,88i, 883'884' 1076,t120,1225'1140'1142''ll#,'1147'1156'1162'1165'1177' 1180,|374,|375,|377,,1381,|4|4,|4g4,1501,1510,1517,1520, A136l 1 5 2 4R, t o , 'A 3 3 ,A 7 5 ,A 9 1 ' A 1 3 5' T21. VariationqlMethods ',205',2}6', [ 1 6 , 3 4 , 6 9 , 7 1 , 7 5 , 7 6 , 7 7 ' 7 8 364'366' ' 1 5 1 ' 1 937 8 'l', 137 g 3' g ' 37 , 26' ( n377' ' Z C390' / 363, 23g,267,2'l2, 27g, 352"366, m', 439', 408, 415'416'418:4lg' 422', !25',438',554',592' 392,401,4fi4,405, 551',552',553', 487',505', 44!,M2, 463,465,4;t" 475' 476:' 623', 624',625', 6-21', 606' 614'617"619' 620', 598,500,601, 602,603; 7 ll',7 13',722', 707', &3'651' 685;696:',700', 6?9, 640,641"' 628,630, 778',779', 7&', 773' 777', 7 55'7 59'7 6'',7 63', 7 24,7 35,7 36,7 39,7 54:' goi gio',857;867', 882', '928',929' '828', 784,787,824,825,g)e"827 l11,6 5 ' ; ;,; , 1 0 0 8 , 1 0 3 0i,o l s ' | | 2 0 , | 7 2 2 . , 1 1 41237 9 3 1 , 9 3 59, 3 5 , 9 5 9 1234,1235,1236, ' 1233', t\72, i205, t207,li08 t214,n2," 1256', 1253', 1219',1251', n47" 1248', 1238 ,1242, 1243,1245,1246' 1308' t307' lzg8, iiso," t251 1285"1289,129,7' 1257,125'd,1251 t385' 1374,ll]le' 1377,i379'_1330,1384' 130g,1314,1332,t34.1', | 5 0 2 , 1 5 0 51, 5 1 31, 5 1 4A, 1 ' 1 3 9 0|,3 9 2 , 1 4 0 5t ,+ t 3 , 1 4 5 5 1, 4 8,i aioe A109',A1lu',Al18' Ar+i' A2, A58, A76,A89'Ag7'Al03' A 1 4 5 ,A l 6 8 l

TOPIC REFERENCES

125

FuncMeromorphic univarent (p-valent) Tz5. coefficient Bounds for tions. 15,215,216,235,264,27i'363'3t'1'372'408'601'619'623'624' 625,629,6t2,709,'141,804'859'866'g24',g25',979',983',985'986', 9 8 7 , 9 9 6 , 1 0 2 0 , 1 0 7 1 , 1 0 7 2 ' 1 0 7 6 ' 1 2 1 4 ' , 1 2 1 5 ' 1 12 53034' 1,1254066''1 2 5 9 ' , |49g,|502,1503, | 3 3 2 , 1 3 3 3, | 3 9 2 , 1 4 5 1, t q s 2 ,1 4 9 0 , 1 5 1 3, A 4 , A g 2 ,A 1 0 6 , A 1 1 9 ' A 1 4 6 1 no (Functionswirosedorr'ain of valueshave T26. tJnrelatedF'trctions Pointsin common)' s79',12851' 4 1 8 ,604,696,77g,82g,830,832,976, [ 4 0 ,4 1, 4 2 , 4 4 ,

T27. Areq Principte(and generalizations)' [5,36,45,51,83,105,107,117'139',141',155',183',205'277'280' 363,4,35,478,509,576,_601,646,682,728,804,831:8.J2,846,881' g25,1C09.1082,1187,!lg2'1193'1194',1195',1198'1267',1286' , l3g4' A62'A1001 1323,1327 , 1332,1333 (suchas Besselfunctions)' Functiorzs T28. univqlenceof special [161,171,1'72,200,201,213'243'321',34g'535',536',540'541', 542,652,686,738,748,750'751'752',753',885',916',917',1109' 1110,1112,1147,1161,1176'1398'lML'1478',1511',1512',A48', A1251 valuesof functionals)' of variabitity(of coefficients; T2g. Regions 1 3 1 , 3 2 , 3 3 , 3 4 , 4 6 , 6 0 , 6 3 , 7 8 ' r1', l7-'13 3 ' , 7163', 7 07' ,65', 1 77882', ' , Z7H ',287',399' 84', 723', 60 62'0', 5i, 55;,590', 404,M8,472, 523,5 8 2 6 , 8 2 8 , 8 3 0 , g 7 g , 1 0 3 , 8 , 1 1 1 4 , | | 2 5 ,A3', | 2 0 5A9', , ! 2 0A32', 7 , | 2A78', 25,t2?5,|239' 1502', 1454', 1413 138t, ' 1374, 1261,1340, A 1 0 8 ,A 1 1 3 ,A l 2 4 l Functions' T30. CoefficientBoundsfor Bounded 1 1 9 4 , 2 5 5 , 2 6 1 , 3 7 g , 4 1 2 , 5 8 3 A1171 '586'587'866',979',1073',1097',1098', 1144,tzot, 1309,1455,A25'A58' = 0' DifferentialEquationw" + pw Derivative-The T31. schwarzian [38,89,90,91,1'71,172,193'335'336',4g2',536',728'786',8M',

126

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

8 ' , 1 6 , g ' 1 1 , 9 8 0 , 9 8 1 , 9 8 2 ' 1 0 4 6 ' 1 0A5185' 101'A,6106' 5, 1'A216656' 1 ,1267',1273',1364', A149', A 1 4 8 ' a s s ' A 5 4 , A 5 2 , A 5 3 , ^2g, T32.UnivalentPolynomials_RemakSeries_HurwitzClass. 152,175,177,!7g,18-0-'l8l'202',210',242',330'533',651'678',848', 8 4 9 , 8 5 0 , 9 4 6 , g 4 ' 7 , 1 0 0 1 ' 1 0 0 2 ' , 1 0A66l 03',1004'1036',1067'1124'1139' A47', A36', L4g6' 1301 ' 1267, 1145, 1266, Functions(andgeneraiizations)' T33. Mean-valent (36,45,51,138,14!'145'146'147',360',3g3',50:'507',512',521', 522,610,614,756,'786'7g2'g25',1009'r00q',1322',1325'1326', 1328,13301 132'1, Functions(f(z)f?') + l)' T34. Bieberbach-Eilenberg , 1 16' ,2 7' ,7 3 7' ,8 0 5 '8, 0 6 ' , 3 1 9 '4 ^ 3 r6' 0 5 ' 6 l l ' 7 4 4 , , 2 2 8 , 2 7 5 ' 4 l , [40, A60al 8 3 3 ,8 3 4 ,8 3 5 ,8 7 0 ,1 1 8 61' 2 8 8 ' , T35. Curvature,Level Curves

'786'

95' 533' 6 6 r , 6 6 3 ,7 3 1 , 7 3 2 , 7 3 4 ' - ] A1411 l2g,l0g, 247,255,?91' 1521' tM4. 1462,l5\7, i o : r , 1 1 0 41,1 3 8 , 1 2' 2l 273 l ' l4r; ,

StarlikeFunctions' T36. CoefficientBoundsfor 1 3 2 , 5 5 , 9 2 , 2 1 ' 1 , 2 3 5 ' ? 5 51071 ' 2 6',11',01i', ' 4 0 01073', ' , 4 3 01075 ' , 4 3' 11076', ' 5 5 21105' ',67'.1',846'888' 1022', 996' 986,990, 898,985, l 3 l 7' 1 2 6 7 ' l l ! 7 : i r s + ' 1 1 5 9 l' 2 l 5 ' 1 1 0 61, 1 0 71, 1 0.8l l 4 2 ' l l w ' , A91l 1427,1433,l44g,1504'15C6' Lemma(andgeneraliza'tions) T37. schwarZ's ' 14' 5 '?, 8 '5' ,8 i ' 6 9 4 8 l g l ' 3 2 0 ' 3 6 9 ' , a 8 1 l 0 ' 2 ' 1 , 2 1 , 4 3 , 8 ? , ? 8 ' [ 1 0 ,I g.r.r,956,964,96g,giz,ro'gg,lllg,'tlrg,ll82,1l83'1278'1341' 13661 ConvexFunctions' T38. CoefficientBoundsfor 1131' 1 2 1 7 , 2 3 5 , 2 5 5 , 2 6 1 ' - 3 4 91 '130555r-1435''A65 -'i'4o , 3o0' l' l,0473'11' ,1505'82l 'l ,2696' 0 ' 6 8 7 ' 8 5 9 ' , 8 8 8 ' 8 9 8 ,1 0 7,11 0 7 2 , 1 0 1 ; t' b z s ' A1401 , Ag2'All7' t142,ll4, 1222,-l3li 1340' 1132, on amplitudes' coefficients(restrictions T39. speciarconditionson the

TOPIC REFERENCES

I21

realcoefficients)' moduli,g&PS, 134,49,71,103,105,208,211,241'242',280'283'284'295',296' z g i , 3 2 g , 3 6 4 , 3 7 5 , 3 8 1 , 3 8 3 , 4 0 8g52',853 ' 4 1 6 ' 4 3859' 0 ' , 4861' 3 1 '888' , M 5901' ',562',563',566' ' 5, i28,'/98,804, 60j, 621,638,64i,C,'7 9?A,986,gg7,1020,1036,1038'1071',1120',1i33'1149'1152' 1 1 5 5 , 1 1 5 6 , 1 1 5 ? , 1 1 5 9 , 1 1 8 7 , 1 2 0 0 ' l 2 l l l' 41l232' 41 '4132061' ,54'3112'7 5 ' 1 2 E 4 ' l g, o ' l 3 8 l ' 1 4 0 3 ' 1 3 0 11, 3 0 ,9l i q g " 1 3 6 2 ' , 1 3 6r 8 Ag4',A98',All6j lML, 1497,A2l, xzz, A47,A86' T40. StarlikeIn OneDirection' 1430' ll42' t147,1166,1212,lzli , 1427, 1108, 1022,1028, [660, 1 4 3 3A, 1 2 1 1 T4i. ConvexIn OneDirection'

1142,ll4y'.,1155'

ll2g, ,301, 660,911'1022,I 105, 1522,Al 17,A1341 t235,238,257 1428, , i tse, llsi, 1160,1162,1212,1337

(

ConiectureI a"I T42. Bieberbach , 8 42' 0 5' , 2 0 7' ,2 4 2 '2, 4 6 ' a',5 7 , 7 7 , 8 1 , ! 1 7' 1 1 9 'I 2 2 ' 1 161,72,73,7 5I1' 495', 440',M5', ', 428',431', 363,373,38i' 407 247,267 ,268,269,' 788',793 , 73;' nd' 73g' ?80',?81', , 643,651 5l'l, 521,629,639 888' 869'882' "794', 862,863, g0g,g09,g33,g34,835,844,846:,852,,853, 1146' 1143 ', \129' 1142', 990;lw\', r1-06-', 903,906, g07,-934,984, 1187,1234,1245,1247,1248,1250'1255,',-1280',1317',t329',1349', 1368,1369,1374,137q1380,1425',1450',1479',1490'A7',Al7' Al05l nrt , A64,A76,A85,A91, A101' (p-valency)' T43. Radiusof Schlichtness i6,i,25'17'1'22't751!76'179'180'182'240'242'256'259'263' 3 3 0 , 3 4 8 , 3 5 1 , 3 5 4 , 5 0 0 , 5 0 2 ' 5 4 0 ' , 5 5682', 7 ' 5 5 8',' 7 , 552', 6 0791 ' , 5' -799 6 7'' , 5 6 3 ' 5 6 4 ' , 5 6 6 ' , 672',', 7-33 &l ',651; 637 ,Llg' 572,595, 568,570, ', 1000', gig' gqz',g70', 88;' 901' 916', ?75',997 800,804, 877,887, 1 0 0 9 , | 0 2 4 , 1 0 3 5 , 1 1 1 3 , , 1 1 3 9 , 1 1 55671 3,|221,1280,|3|2,|367,1369, ' A92' Al22' 1495,ti9g"A4E, A68, A'11 Articles' TM. SurveY 8 8 6 ,9 3 9 ' 403, 4ll' 514',115' 5 3 7, 6 1 8 , 8 6 4 , 23g, 126, 125, [1M, A ? A ,A 5 l , A 1 1 5 ,A 1 6 3 1400', g78,106;,!240,1241,1305'1331', (ChaPter6)l

-I

128

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

T45. Odd Univslent Functions. 295, 296, 3M, 363, 137,49, 70, 75, 184, 207,208, 241,242, 268, 3 6 5 ,3 7 4 , ' 3 g g4,1 3 , 5 1 95, 5 7 , 5 6 15, 6 5 ,5 9 5 ,6 2 5 ,6 3 7 , 6 3 86, 4 1 ,6 7 5 , 72g, 733, 731,804, 812, 8M, 846,863,865, 888, 953, 967, 1022, 10811 , 1 4 0 ,1 1 4 ,1l l 4 7 , l l 4 g , 1 1 9 0 ,1 1 9 2 1, 1 9 3 , 1 1 9 4 , 1 1 9151, 9 8 , 1200,1233,1325,1340,1368,1370,1426,14501 T46. Angular Derivative, SphericalDerivative, Invariant Derivative. 6 4 7 ,6 4 8 , 6 5 0 , t 1 9 3, 2 5 0 , 2 5 1 , 2 5 2 , 3 0 83, 1 1 , 3 1 2 , 3 1 3 ,5 2 8 ,6 2 0 , 1278,1330, t409, 1410,1436,1438, 725,839, g4g, 1008, lw, 1445,1446,14g7,l1bi, 1469,A20, A72, A73, A162, A167l T47. Convolution (Faltung)of Functions 985, 1031,1063, u43, 145,22g, 230,278, 198,518,7 19,721,869, , l 1 , A 1 4 3 , A 1 4 4 ,A 1 6 0 ,A 1 6 4 1 1071 , 1 1 5 7 , 1 1 6 4 ,1 2 7 0 ,1 4 7 7A T48. SchlichtIn An Annulus. 1 24 , , 5 , 5 4 ,2 3 1 ,2 5 5 ,2 6 5 ,2 6 6 ,3 4 6 ,5 4 9 ,7 \ 4 , 7 1 8 , 1054,1432,1518,A2, A34,A40l

7 8 4 ,9 2 1 ,1 0 5 3 '

T4g. SpecialGeometry of the Mapping (such as k-fold symmetry)' 234,255,260,261' 133,34.40, 56, 57, 78, 106, 123,133,I 38, 221, 301,305,3C6,322,352,367,383,434,458,474,179,480,487,546, 562,566,570,572,573,577,578,579,580,587,588,589,ffi7, 625' 7 32,7 34,770, 778, 77g, 7 89,7 93, 795,7 96, 8 I 6, 8M, 932', 654,660, 941,950,976, g9g,1002,1M2,1043, 1049,1062,l07l , 1072,1093' , 4 f , i 61,4 3 0 ' 1 1 3 0 ,1 1 5 1 ,1 1 5 8 , 1 2 1 6 , l 2 l g , 1 2 . 1 5 , 1 3 4 51 ,3 8 1 , l ? 8 2 1 1 5 1 7 , A 7 4 , A 1 4 7 ,A l 5 8 l 1431 , I M g , 1 4 8 2 , 1 4 8 4 , 1 4 8 61, 4 9 4 , 1 4 9, 8 T50. coefficient Bcunds for p-valent Functions. | 4 8 , 9 2 , 1 3 52, 5 5, 2 6 | 3 0 5, 3 7 6 , 3 8 8 ,3 8 9 ,3 9 6 , 4 2 8 , 4 3 0 , 4 3 | , 4 4 5 , 4 9 6 , 5 0 5 ,5 7 6 ,5 7 g , 6 8 2 ,6 8 4 ,1 0 1 9 ,1 0 2 0 ,1 0 2 4 ,1 1 5 0 ,l l 5 l , l t 5 4 ' 1 1 5 8 ,i 1 5 9 , 1 2 1 5 , 1 4 2 7 ) T5l. Coefficient Boundsfor Typically-RealFunctions. 715,9Ci, 995', [55, l7O, 31), 374, 375, 413, 432, 436, 44i5,580, 1022,I140, ll4r' , ll47 , 1i49, 1152,I 158,I159. 1431, A^71

TOPIC REFERENCES

I29

Odd UnivatentFunctions'

T52. CoefficientBoundsfor 374,ql3' 5l?' 363,365, 304, 242' 241', 208, 84,207, I 11?9' 137,49,70, n4t, ll47, 1152, 1 0 8 1irad, ' l o 2 2 ' 8 6 5 , g M , 8 4 6 , 8 6 3 , bli, 1325,1368,1426,14501 1 2 o o 1233" ' 1tgi,11931 , 1 9 41, 1 9 51, 1 9 8 ' Grunsky T53. Faber Polynomials'

Coefficients

95'l', 571', 363',393',!16',485',554-', '569', 205,234,261, |342, |332, [141, ?61' |272,1286, t'zsg, l,zso,.|25s, 958.|02g,|24.7,1248, l4l5,l4gl,A27'A23'A55'A62'A69'Alt)O'Al14'Al42l

T 5 4 . C o e f f i c i e n t B o u n d s f o r t h e C l a1' s swith ( S ) ( t h e c=l a s0'' ^f o'(0) | f u n=c t i!o' n s " f ( z ) /(0) < in i le univalent and regular 1 7 2 , 7 5 . 1 0 7 , 1 ! ' 7 , 1 8 4 ' 2 0 5 ' 2 0 6 ' , 2 4 1 , '568'12?' , 2 4 2 ' 2 6619' ? ' , T651 ^ \ ' ,'654' 329',363',364' 407'qoi'iit' 51i '5-?l'567' 8'3'3' 365,394,400, 834',846'906' 7g3' 804'

- , ' 1 1 478g 4 , |loo'', 727 1190' ,728,7 40,755,i 6;"2g8', l l 4 6 ^ _ i i s o1, 1 5 41, 1 5 5 1' 1 8 9 ' 1 0 7 5 g 0 . 7 , g 51g0, 3 g , ' 2 0 31' 2 3 3 ' l' \ 2 1 ' r 1 9 8 '1 1 9 91' 2 0 0 1 l l 9 t 6 1 1 9 5 , 1 1 9 4 , lrgz,t193, 1381'1396' 137',7', rJz;"ills '13'!',137s'', "475', t234. 1250,1284, A46',A111',Al 19', 11431 l'479 ' A5:i' 145?, 1426,1450,

Fractions' T55. Continued 1 0 3 5A' 4 9 l t 9 1 3, 9 1 4 , 9 1 59,\ 6 ' T56.DistortionT.heoremsforFunctionsofPositiveRealPart. A31' A94] 1154'1320', [887, 1144,1147, T5T.UnivalencyoverRegionaotherthantheL]nitCircle [ 5 0 , 4 7 1 , 1 0 5 9 , 1 1 5 0 ' 1 2 ! 2A42', ' l 2 ]A1311 -1','1302',1303',1304',1363',1398', 1488,1489,Al8' A40' 148',7, (Jnivalent(p-valent)FuncMeromorphic Theorems for T5g. Distortion tions' 1 5 , ' t 3 , 7 4 , ' , l 5 , 7 6 ' 1 5 5 ' 2 0 9 ' ;44',595', 3 8 ? : 3 9 0697 ' , 3'709 9 5 '',712', , 3 9 ' ,8M', 7 : 4 0881', 0'404',407',408' 455 ',481',422,426'ili' 1333' 416,418, 1332', 1316' 131-3'' 1076,rosl' llzi', 118-;',nss', 921,1071, A1591 17 ' A35' Al ' A146' 148| ' ;;;; '-1513 1390' 1397,

130

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

T59. Relsted Results from Analytic Function Theory. 8 4 '8 5 '96' [ 8 , 9 , 1 2 ,1 3 , 1 41, 5 , 1 71, 8 ,1 g , 2 7 , 5 9 , 6 2 , 6 6 ' ' 9 3 ' 9146' 9551 66' ' 1 6 3 1 6 0 , 1 6 2 , , l & ' l l 2 , l 1 3 , l l . 4 , l 1 5 1, 2 7, 1 5 3 ,I 5 4 , 1 5 9 , 2 2 5, 2 2 4 , 2 2 3 , , 22, , 9 0 |, 9 2 ,| g 5 ,2 | 0 , 2 | 4 ,2 | 9 , 2 2 0 2 , 881 1 8 5 ,1 8 7 1 232,2M, 245,248,24g,273, 276, 286,287,291,292,298,299,302, 332,334,340,343,3M, 345, 303,3|4,316,319,323,324,326,331, , 7 , M 9 ' 4 5 0 ' 4 5 1 '4 5 7 ' , 6 1 ,3 6 2 , 3 9 8n,2 , 4 2 5M 3 4 7 , 3 5 7 , 3 5385, 9 3 504,506'510'513' 464,466,486,4gl, 494,497,499,501, 45g,462:, , 8 2 .5 9 3 , , 4 8 , 5 5 55,5 6 5 , 2 g , 5 3 15,3 4 , 5 3 55,3 9 ,5 4 7 5 , 275 5205 , 255 649,657 ' 658' 632,633,634,635, 5g4,5g7 ,608,609,616,622,631, 695,699,701'702'7A4'706' 666,667,669,670, 671,688,689,690, ' 37', , 8 3 , 8 1 ,8 1 7 ,8 1 8 ,8 1 9 ,8 2 3 8 7 2 6 ,n 0 : ,7 4 A , 7 4 57,7 1 , 7 7 57,7 6 7 938' 871,878,895,900,9M, 905,920,930, 840,841,845,847,860, ggl, 1014, 101 3, 1012, 994, 992, g44,g4S:,948, 962,966,969,973, 1 0 4 5 , l M 7 , 1 0 5 21, 0 5 61, 0 6 0 , 1 0 4 0 , 1 0 3 9 , 1 0 1 5t,o i z , t 0 2 6 , 1 0 3 4 . 1084,1086,1087,1089,1096,1100, 1061,1065,1066,1074,1077, n34, 1135,1136,1137,1188,1204,1206,1223,1226, llll, 1126:, 1282' 1252,1261,1262,1264,1268,1269,1271, 1274,1277,1281, 1351' | 2 8 7, 1 ' 2 9 4| 2, ,g 7 ,1 3 1 11, 3 1 81, 3 2 | ,| 3 3 4 ,1 3 3 6|,3 M , 1 3 5 0 , 1 3 9 31, 4 1 1|I4, 2 2 ,| M i , 1 3 5,3| 3 5 4 . , 1 3,5 15 3 5 71, 3 5 9|,3 7 3 ,1 3 8 8 , , 7 0 ,| 4 7 2 ,| 4 7 3 , | # B , | 4 5 7 ,1 4 5 81, 4 6 0|,4 5 : - |, 4 6 5 ,| 4 6 6 , 1 4 6 8| 4 A50' | 4 1 5 ,| 4 g 2 ,| 4 g 3 , 1 5 2 5|,5 2 6 ,A 1 3 ,A 1 6 ,A l 9 , A 4 3 ,A M , A 154, A 1 5 3 , , I l 3 , A | 2 9 ,A | 3 2 , A 5 7 ,A 6 l , A 6 3 ,A 3 2 ,A ^ 8 4A, 1 1 2 A , 1 5 7 ,A 1 6 1 1 A i 5 5 ,A 1 5 6 A Domains' T60. UnivalentFunctionsin Multipty-Connected ' 72', 4 6 9 '4 7 0 '4 7 1 4 [ 1 ] , 3 9 , 4 5 , 4 7 , 2 7 7 , 3 2 0 , 3 7 7 , 3 8476,7 , 4 6 8 , 7 54, |0, 7 708, 473, 482,502,596,615, 6|7,691, 692,693,707, 477, g 2 7 , 9 6 39, 7 7 , 1 0 5 01' 0 7 81' ,0 8 0 ' , 7 6 9 , 8 1 58, 2 1 , 8 5 78,9 9 ,9 1 9 ,9 2 6 , , 1434,l4&', i08E, 1127,1128 , 1254,1298,1316,1343,1386,1387 A6, A40,A61,A151,Ll52l for BoundedFunctions' T61. DistortionTheorems 5 7 3 , 5 8 55, 9 0 ,5 9 1 ,& | ' 1 2 4 2 , 2 5 53,6 9 , 3 9 64,| 2 , 4 8 2 , 5 0 55, 3 2 , ||M, 7 5 8 ,7 5 g , 7 6 0 , 8 2 6 , 8 6976,5 , 1 0 5, 1| c 9 7 ,1 0 9 8|,| 0 2 , 1 1 0,3 1172,11913 , i 3 ,1 3 4 81, 3 9 0 \, 4 5 6 ,A 2 5 ,A l 3 0 l T62. BoundaryBehavictrof univalentFunctionsg, 3I 8, 341'342'346',348', [23,178, 221,236,237,253,27 308,3!7,

TOPIC REFERENCES

ral

5 1 1 , 5 2 2 , 6 1 3 , 6 5 5 , 7 0 0 , 7 5 7 ' , 81280' 7 2 ' , 81343' ? 3 ' 81408' 7 4 ' , 8i410' 7 5 ' ,1486' !044',1079',1115', l27g' 1r16, llz4,l l43, 1146,lnz: A8l generalizaStarlike Fttnctions(inciuding for Tkeorenis Tb3. Drsrcrtion tions of starlikeness)'

6-1',7 ' 353'356,431,134,661, ,26A1?61',282', 157,255,258 142, 1154, 192, , ll4y' , ll4'7, 10]6'1108 1071 ' 1073', 896,-8g;,953, 716,853, A37' A38' A ?1 , A 9 1 ,A 1 2 1 1 l4g4' 1267,1340, 142:7,l'Ui}'

T64. Distortion Thet'remsfor tions of convexitY)'

C onvex Functions

(includir'g general\za-

661' 356,383,431,453':19' 355, 261, 255, 247 e63' ?9?' u 18, 142, , ;;i; 884;8e6,8s7,eoe'es3'A65 766' 762' jt6, 76r, iz3, ' ;8r,' 1510' ;;6, t43s' 148l, 1494, 144' r o l i , 1 0 9 51, 1 0 8 ,11 31 , 1 A67,A78,All7l

p-valent Functions' T55. Distortion Theoremsfor 75 60 85 '733'','73 1 4 8 , g 2 , 1 5 ? , 1 g ' 7 , 2 4 6 ' 2 5 5 ' 2 5 8 ' , 2 6 . :6 2 8 32 ''6, 8 34 7 '56'9, 3 6' ,36',7'3'76',, ';tt' 3 8 8 , 3 8 9 ,4 1 i , 5 0 5 ' 5 0 1 : ; M ' e w ' € 8 0A38l 1435', A37' 115C,rrsr',-l'154,1427' T66.DistortionTheoremsforTypicalty-RealFunctions. [4,170,375,413,415'427',436'626',858',953',1053',!125',1144', ll47 , ll4g, 1427,A41l odd univalent Functions' T67. Distortion Theoremsfor 1340',14261 557'733'804"953' 1147', 75,3gg,519' ?0, [49, the C/ass(S)' T68. Distortion Theoremsfor 383' 234',246',2!',281'306', 142:156', 71,'75,79,118' 68, 507' 500', 164,65,

415',453',115'484' 400', 394,ly)j,-igg', 19;', 828'833' 385,386,390, 826',', 7g3:'q04' 7ll"1za"74z|;l',zae', 599" g5g 557 ,558,559, ' 989'1006' gggg\z' 940'951 1 852';;;'g0o' 846, 834,835, 118e'r22s' rrl?:-1175', 11s+', n4',6;,1t.t^g' n;;, , 1008,1030,1051 11431 " 1426', 1425', 1339 1280, ,l3'14'1375'1396',

h-

I32

BTBLIOGRAPHYOF SCHLICHT FUNCTIONS

Corrections in the bibriographyindicatingdupliFollowing is a rist of references cationsor translationsof the samepapers'

Reference 389 426 476 559 565 s66 568 702 708 806 850 1145 r260 i292 1497

sameas

Reference 388 422 475 558 561 :62 567 70r 7M 805 848

rr43 I258 1289 2lr

ce 287: Erzohi should be Ezrohi Notes (a) R.eferen is sarneauthor as Lowner' K . Co)Reference869: Loewner, C.

^l

CONTENTS

133

BIBLIOGRAPFIYOF SCHLICHT FLINCTIONS PART II (1966-1975)

CONTENTS Preface BibliograPhY Topic References' 1966 T a b l el . R e f e r e n c e s P r i o r t o f : 1 t Year 1976 Table 2. Refertnttt in

t34 137 254 270

27r 27r P:!ltthtg*1tJ"":il;; Referen-ct: :' :'': . : . : : : : 27r rablel. Numitt "r (MR)Numbers Review

;ili:i. #r"iTddiil; vratt'. Correcilons

..::....

273

134

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

PREFACE

of univalent (Schlicht)funcThe first extensivebibliography in the field 1966.It is titled Bibliography tions was publisheciby this *rit., in May lviaihematicalSciences,New of schlicht Functions [courant Institute oi 41-019' IMM 351 (1966) York University, TechnicalReport I'lo' NRO to it as BibliograpiryI. Bibliix* 157pp.; MR i4 #zg4gj. w; shall rcfer the years 1907 (when the ogiaphy I connins i6g4 referencescovering the year 1965' and infirst substantialresultswere published)through papersappeared in 220mathemacludesthe work of 570 aurhorswhose of Schlichtfunctionsare' tical journais. Ttre variousresultsin the theory and cross-indexlistingsare in BiblicgraphyI, classifiedinto 6g subtopics Thus, eachsubtopicis followed given betweenreferencesand subtopics' 'ro that subtopic' and conversely' by a list of those referencespertaining subtopics dealt with in that forowing each referenceis a list of those reference.

PREFACE

135

to. Brbliograp'y i by individual reception The favorabre _given and industrial sutdcnts,oniu.rJiv iiuiuties, graduate mathematicians, *riter tt continuethe Oaborious) researchlaboratoriesencoururJ,his andcatarogr,ring the periodicflow rrurrTir.afion topic rea,.ling, effo'ts have collection, th: past tc,, yeais.These d,rring papers research of schlicht of new of the pr.r.ni Bibliography culminatedwith the publication as BibliographyII' we refer srrbslq,rently part which to II, of 523 Functions, refer.n..=rtothe publications 1563 contalns II Bibliography journalsandpublistring in 200mathernatical apeareci have which authors England'Germany'France' lnitr. u.s.e., tne ioviet Union, many symccmpanies other countries.It includes many in and China, technical Japan, dissertations,abstracts, univalent posiums, colioquiums,"o,,g,.,,.,, of f,ool,, dealing*i'tt the-theory reports,t..trrr.Ior.r, and o1^ *ole and mlltiply-connected (Schlicht)and multival.n, .uoping, 1966through r975' somepapers vJurr in domains.This survey.ou.rr-rrr. and which were not includedthe tieo rhe to v"i prior pubrished publishedin in Tabrer. Somepapers riri.a now y are i Bibriograpt

havebeen functions v.u' rs76"'.jlT11J;l:1lti;; theory of schricht sixty-eight

The first in BibliographyII, into nil:ll,uuiopits' I' The additionalsubclassifred, sameasin Bibli;;;aphy place9utof thesesubtt,picsaretrre or emphai, ittut rravetaKen deverop-.nr, n.* topicsreflect listingsareglven I, cross-index Bibliography o;i" years. ilexamples ing the our,'i* rt.,,, ittt rouowingtwo ,uuiopi.r. and references between of the Bibliography' of Schlicht lustratcthe principaluse firt';'Juau*ard products tiiot f Refer.n.. S' Examplel. by Ruscheweyh' ;;;;lt"' p6lya-Sctoenberg Math' functionsand the commen'+-' rhis r. ;;; is to paper andshe'-Smar, "nn.{i.^jii:i{':::,11i t:"tt*.of this 11_1-13:..A p"L.r s1\, year 4g, Helv.,votume (MR) of the AmericanMathenraticai nl"i.*, Niathematical 2' 4' in be found rhelnrr*bt's in bracketsll' olgt. * revi.* 4g, subSociety,Volume .onrui"u inrotmationregarding 6al indicatethat ,iri, pup., tovicsr t J4 inrerestedin Bieberbach-Eilenberg ]oi;;;.;].T;T : as T34' The will find;;i; subtopiclisted regarding relared.r"*.rl (or funcrions thatinformation rg,'.".-.', r493rinoi.ut" is a paper by bracketedreferences in i.r.l.-n* t9r rvhich iouna be may this subtopic paperby volgnec' fi+gil wtricnis a . ' ';tft"ntt A" Dov' Aharonov, I. A. into subtopicswasbased rcferences various the of the The crassification r.r'-rengthpapers),and for reprints tor reading on a deta'ed "i'g5

136

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

reviews' or of their(brief) abstractsor remainingreferenceson a reading authors' Therefore' in fairnessto the (in a few cases)from the titles ""rv' complete the do not alwaysindicate we emphasizeitru, the crassifications

eshavei:'::i::-': :l::1TT.j",:, enc " "1 ::Jl;ri#:T rhererer fall simply did not ?;; infornration or the contents

either to lack of avaitable the ninety subtopics' within the fixeOframework of T h e r e f e r e n c e s i n c l u d e | 5 2 a b s t r a c t s . S o perhaps m e o f t h under e s e w ea rdifenever published been have may others pubrishedin fu', have appeared while others are too recentto co-authorship, or titre ferent no Math' Review(MR) numhers' in full. Abstracts,of course''have have referenceswhich ate not abstracts One hundred and thirtylt*o notes, dissertatutuny of them are recture no Math. Review numbers'. published' or too reports' papers not yet special anO technicat tions, in the Reviews' recently puUtisttedfor inclusion published nature to cover everypaper It is difficult in a work of this omissions are functions' Reasons for on the subject of Schlicht ingo*.uer, it is felt that this bibliographydoes numerousand varied. yearsfollowing p*blications during the ten cluclea major portion of the

sutdents' theaidgivenmebv twograduate mein "totti;#o.lJ,,i; acknowledge assisted who Elmasriuriaur. AnthonyDiNardo, looking up MR' Mr. Mohammed papers' of

hundreds locating lournals, photocfoyi"s clerical tasks' referencesand nulnerous other Igivemanythanksalstltothemostcooperativepersonnelofthead. of library of the courant Insfitute of mirably stocked mathematicsyork university, and to the Director New at Sciences Mathematicar my sincere plsfsssor Peter Lax' Finally' I wish to-express the Institute, of south w. Goodman of the university e. Professor to appreciation cemplete this during the past ten years to Florida who encouragedme brbliograPhY' S. D' Bernardi March 1977

BIBLIOGRAPHY OF

(PART II) SCHLICHT FUNCTIONS

137

BIBLIOGRAPHY OF SCHLICHTFUNCTIONS (PART II)

l.Abe,H.onmeromorphicandcircumferentially-y:onunivalent function,.l.Math.Soc.lupun16(1964),1+z-lsl;MR31#238.7.|9,

in ctass of theBazitevic Functions A. . L Aksent,ev, o z. i^;Ji;,3i]u. ;

thediscandinanannulus.(Russian)D o k ! . lDokl' k l d N a15(1974)' ukSSSr 50 $+eg. [SovietMath' 2t4(1g74),24t-244;MR

,. f;,1?;

tii*xt.,

andreat-vatued comptex between A controst

Taytorseries.J.Austral.Math.Soc.l8(1vi+1,458-460;MR51 of power series(Ruson convotutions theorems certain f:,ij;,"rl] -. fuut uzSSRSer' Fiz'-Mat' Akad. Summarv).-tzv. sian.uzbek 10' 22' 471 no' 5' 5-lit ftf* 33 #5902'lI' Nauk9(1965), conformsl of the *ri,i of uniylleil qurrrion, certain H. 5. Acilov, mappings.(Russian.UzbekSummary)Izv.Aiad.NaukUzSSRSer. no' 5' 3-9; MR 34 #2848't4l Fiz.-Mat.Nauk 10(19d;

138

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

on an areally mean p-valent function' 6. Aharonov, Dov. A remark IsraelJ. Math' 6(1968)'I19-120' [33] Haymon. of Cartwright, Spencerand 7. Aharonov, Dov . The theoremgig)' ' #4377 t33l MR 3e

Math'soc iiliir J. London

\?-1t6;conditionfor univalence g. Aharonov,Dov. A *rr;;;;;; and,sufficient ofomeromorphicfunction.o,,t..Math.J.36(1969),599_604;MR 3 ,U 4 0# 2 8 6 5 . 1 4 , 9 of o theoremof Jenkins'Math' g. Aharonov,Dov. A generalization 34'861 ' ze\t.r rotiqiql, zt8-zz2;MR40#325'127

l0.Aharonov,Dov.Anoteonslitmappings.Bull.Amer.Math.Soc.

' [531 i:e -839;MR 4r #3725' 7s(l96e), Func*ons. Bull., . on BieberbachE,enberg

r 1. Aharonov, Dov A . N I . S . , 7 6 ( 1 9 7 0 ) , 1 0 1 - 1 0 4 ; M R 4 l # conjccture l g g 4 ' 1 3 4for ' 8 6a' 8certoin 71 prool-iy'rn, Bieberboch . Dov rz. Aharonov, J. of Math. 8(1970),102-lM; fun,ctions.Israel of univalent class MR 42 #486.139,421 of for univalence conditions of necessary 43 13. Aharonov,Dov. sequence puke Math. l. :g(r 97l), 595-598;MR function meromorphic #5015. t31, 53, 541 , . : ^ ^ r - . - n f n r f r t n r - t i n / t sw itl a for functionswith conjecture Bierberbach the on . Dov 14. Aharonov, Journa!of M;th. IS, no. 2(1973), smallsecondcoeffic:ent.Israel l3'7-t39;MR 48 #520'142'541 Duke of flnllions snd relatedclasses' 15. Aharonov,Dov. on pairi 8 6 4 7 # 8 8 3 7|.2 , 2 | , 2 6 , 3 4 , ,8 7 ] M R g 7 3 ) , e a o l o ; 4 0 ( l J . Math. with the s' ott an inequalityconnected 16. Aharonov,Dov.; Friedland, coefficientconjectureforfuncti\,:ofbouna:d.|:undoryrotation. Ann.Acad.Sci.Fenn.s.,.A.I.rvrutt'.,flc.524(|972),|4pp.u,1|, 'larY 771;MR 48 #519 ^ ,\, :,.-^tinnooj ,,f baunded h, bouna on S. functions pp' |7 . Aharonov, D,; Friedland, Ai Mat' no' 585(1974)'18 ser' Fenn' Sci. rotation Ann. Acad'

w' E.1'*:'!oo,:{,1#:"::;::ion'ar'c 18.lll'*"""v, Dov;Kirwan' applications.I.Trans.Amer.Math.Soc.163(1g72),369_377;l'{R 4 5 # 5 1 6 .[ 1g , 2 4 , 3 4 ' 3 5 ] lg.Aharonov,Dov;Kirwan,w'E'Amethodo'fsymmetrizationana ttpplications.Il.Trans.Amer'vratt','Soc'169(1g'72)'279-291;MR

19,241 47#2CA2.u6, 4|r c l a s s e s o l z o . A h a r o n o v , D o v ; K i r w a n , wMath. . E . C zittgl3), o v e r i n g4|2-4119; theorem sfo MR

yniyqie,i;fimction,. Ca,,ad.J. qoo. #2M1.[6, 10, 19] betweenthe coefficientsazand inequatity An v. Lars Ahlfors, 21.

BIBLIOGRAPHYoFSCHLICHTFUNCTIONS(PARTII)139

certain problemsof Mathernatics a univarentfunctio;:. (Russian). r'Aut' "Nauka"' Leningrad' ;;.-'l(l+' and Mechanics(Russian;,

s; topics in geometricfunuicn nt r i u v s n i r ila ti "Jt .ttij,;ii zz. f;$;x

t l r c o r y . M c G r a w . H i l l S e r i e s i n l { i g h e r M a t h e n r a t|973. i c s . MIX c G+r a157 w-Hiii York-Dusseldorf-Johannesburg, New Book Co.,

,r.

oJnir}l

:.#\t);,),ii),

functionswithquasiconfor.ma.t onschticht Analysis

the sympl'ium on connplex extensions.proceedingsof LondonMath' Scc' Leclgtl)' Canterbu'L P-p'1-t0' (Univ. Kettt, London' 1974' '.urcNoiesSer'' No' I ; C^^;'*t^t }Jdu' Press' to Jf tn, principteof theergumeni p-.A, L. 24.rrkserrr,ev, Vtss Ucebn' "io,tl.-": f Jl' the study of univatrnr'['conditiont. l-rs; MR 39 #7078'[28',57] ;",.12 (7g)., tqig, "1Rt'ssian; theargumentto zaved.Marematika i theprincinleof oip'titirion An A. L. Aksent,eV, Ucebn' 25. tnustiu") yu' vvss' univatrnr{rinrditioni.lt' of the study MR 39 #7079'[28' 57] atika 19'6;'no't (Sa' l-tS; ZavedI'4aterT of inverseboundaryvalue sor,.,abitity u"niror*tt The A. L. 10(1973), 26.Aksent,ev, Sem. Kraev. ZadacamVyp. problems.(Russian)r,ujv ll-24; ivIR 5C#619' 14' 621 funcof univalent closs L' A'; AvhuAit"'F' G' A certain 10 no' . Aksent'eV, 1970' 2'7 u..u1, zaved.Matematika v;r. Izv tions.(Russian) ' [4' 9l (101), 12-20;MR 43 #7607 crite,' critens r],',t V'P v p ' Univalence Univalence V' N'; Uittu' Caidut' A'; L' 28.Aksent'ev,

f o r n - s y m m e f t i c T u " t i o n ' ' G u s sMR i a n )50 I z#4922' v ' V I : Ut4j cebn'Zaved' Matematikarg74,no.+ir+3),'3-13; for a special polynomials of Faber The S. fi. Zg.At-Amiri, l, issueno. 103, ")potii' Math. Soc.,uoi. t5, no. e*.i. Notice,, '1968. .function. .' t53l p ' 145(Abstract) Jun.rurf of order ot. on p.clo,,.,o.,tor functions S. Ha,soon, AI-Amiri, 30. [6',10' 11' 10j-108;MR 43/,'.l608' proc. Amer.Math. il. 29(1911),

o{"::o,t:!::,tJ:{X!'fr{i.'ri';:" ontheradiu' ,,. f,:f?;,ffl"..,25(tg72),Fasc. r, pp.lis-tzo;^rvrn 46#341'122'431 coiloq. Math funco-fuiiuorenceof certainonarytic # 6383' 4 8 32. AI_Amiri,H. s. on thi'iadius M R j g t f g : R ) ' fu " ' 1 ' p p ' 1 3 3 - t 3 9 ; t i o n s . C o l l o qM' a t h '

or runctions orstartike s-convexitv ,t ,, Kil; l?,,'I;Jt;f!;l?;i,X, MR 47 #445' proc. Math. Soc.iqtrgz:1,101-t09; ordera.

Amer.

anatvtic of certain ofstortikeness radius the o, l"lli,?;ir1,ru3l 34.K;

140

SCHLICHT FUNCTIONS BIBLIOGRAPHY OF ,t

functions.Proc.Amer.Math.Soc.42(|974),466-474;MR48#8768.

':"': Roura(ius ?t ffi'{*' fi-1,,:i,lt;it; 3r. ,o!.:::":".?l',i'nr2' < ,',!i 1' Rev' in the circuro,,rgion',- lzl : MR functions univarent [i2,69]; trq'sl, "o.8,863-868. m a i n eM a t h .P u r e so o o i . t i o l 52 #719.

H.S.; Reade, Monatsh llaxwef P.'.-?,1,:.:'':,::":;f:.'iiffi"fl 36Al-Amiri, orent runctions' iiii#r"'"i,:v' ii"ii; !l,if#;,1;,|;;nc' 4 -264,'.1:'J

' .257 *"i:L{,:,o,,n12':,!;::r:i:'{';;{ ?;; T l *;.1'T :{rfr 37Xff'l';l.K' " " 4 #; :,*'# i;'*:1filJ;,it ;:|5,\i?ff',*ii,l": "'1,*; oi{ii,;?ill;$li; -38; ill'i;iLliiiiililT""'#ii')vi"1i1;'{;1*'f -vru,. t75(ts6q,2e 38. . .h {J'",1. M :' K llll"r";i;*ii'IT" Math.80(l975),

il$'

(Russian) of Functionats o.fstsre.ms ronge Vyp' 3' 59-70; ,n. X,tul'u*:::,J11 !!te. Univ."i.'r.t i.h'-ftfu'' tgZ(lqeS)' TrudyTomsk.Gos.

holomorphic N{R 33 #7514' r, \r fnmilv of holomorPhic' V' Aa family O'; Baranova' V' and 40. Aleksandrov, I' iuoltlnian' English ,r**rri

a shift functionswith univatent Ukrain' RSR SerA Xa''^f'^ p"p""iAi fk'i9 Russian'u**u'ies)' ' t49l 46#5591 *l Russrun ,4j5t rglz,lszj;o V' V'; Kufarev' P' O'

Chernikov' MoS article 4l.Aleksandrov,I' A'; no. +; emer. Math. Soc., zo,diiol, vol Surveys, Math.

' tfl' cirulai,slll or.I'*'lTJ"?; l; formula' (Russian) o "t:;, having "::::fni'*:;:'K:'f functtois analytic of [Enelish "'u"'ral Mi 33#5e00 iosirqesi,qij-eso; sssn Nauk eiaa. 6'13',241 2' Dokt. u' Math.n"ii. oitgos),1;11-15351' probtemsfor transl.Soviet itii:"ii'rtii' v' Ja' Extremat (Rts:ian) A'; I' 4S.Aleksandrov' fornt'la' o Tuniticishaving "'u"ural of anatyttc 1l l-122;MR closses isq(tgOO)' Met''-vf"i' Ser. U"i". Gos. Tt,nst<. Trr-rciy classes

'SiUi'lt' i i llg""*'ol' MR 'Lt;' oo'J,ffi :L,'?:I:i*;''r',":r?8::',:{;,'':" rnru''Z' 7(1966)'3-22; functionr.tilri*i",tj tu-convex

Akad' Nauk ,r.I,JfiJ"l'Lt;'u'''T'"3iu'^"'kil,v,Ja;3:"X?f{{;::':IJ furrciicn.,-jqo"ian).Dokl' univateni of the theory r!:"'ir!'}" orvatues or y'"'n *:{"*X;q the ,.'fffi"**:"? f'ncilons of of coe'fficien-': coisistine ?f polynomialexpressions Univ' Stt' Mch'-Mat' i"'Oy

or E' (Russ"D T"*tul'bo'' ciassesS ' 124'291 30 #4925 nuti li-igt z' 175(l96+),vvp'

j

BIBLIOGRAPHY

OF SCHLICHT FUNCTIONS

(PART IT)

l4l

l' A:;K^onan'ev: :;i:';:':fr':':; i-; i; rf!r#Xi";:: 447.Aleksandrov' 68] nt r,nn,zztvs,4e, -r ^ j ,.;1i;it ttl trj.lffi,,{,ft1:[",f,!;:';ii;,q:,;1il;; '':*::::'::;'"illii'y::'{.'J; Areksana'u' 46 48 ,17"?,'lluiiT!{[{:;;+,un tzst.' Miqtg _, of bouna. ii coefficients iil,first ffi .1". andRus;. o., *,i".u";,; 49.Aleksanu,"", functi.ot iliiuiniun'-Bttelish nsx Ser'A 1973' ed hotoiorphic,*iuoiri xai;il;;1t' Dop""iii'e,tao. siansummaries)

*'t'.3J,':: :itrx:,{:;';^;!;i" ,,hjfl#*i Kit;'"li:ftl MR46#5600' o ,r'i;;:it8 ' 283; Dopo-vjai summaries) i"rr*r ull- Rtssian Trrrctionr.(ukrarnr"* nJriT., Akad.Nuui.ukrain. of I' E' o.f^:'.:l':,',',,,Ji o^problem oJ of solufion Solution u, 571 i --. r A';-Iopou' I. v. inurcurves(R l' A pooov.V"I' 51. Aleksandrov' v' Koiickiionstor-iotito t'i"I':vel andG' 30#!202'16'71 Bazitevic

Mat.i.'iir'gisl, to-iit'no* siuirsr,. sian).

52eleksana,oy* l* 13-20(1972); ' (Russtan' f uncfions s.., . u"i\'-'i irqoszT')' Mariaecurie-skroao*Ju MR 50#sez'l24l ""Jij'*rrffiltrJffl{|*'iiil.'"lii" SibirskMat'

53.Aleksandrcv'1'A.ifonova'G"AExtremalpropertiesofunivalent rJ'*tti' reql' offi1l ",^tllssian) horomorphicfunc,,9

sssR i??,:r'"1{f:*'i:;:,:;;,"z",hecurva, ;"-11'Akad'Nauk#2027 ,_iJf,t:j3;lf (RliJ*J' ' sp MR 46 on tne'rta$ Ievetcurves 43,4?1 ,iii|g,il,tr:"*ztiotrgl])'lii; 267269'".rr"rr'*. [6, |0,,29,35,certutn zo3(rg.t'), :lbjioa D?H. for nii'*oJ problems tsovietl(iatt'. o'''solort"'']t'f, '' t!,e.larf-ptane'-(Russian) 55.Aleksandrov' thatareuniv'oir"i"-ii qe#1e88 ' 124'571 of functions i crasses igt-'o?i* 'iti''lol' the'variational on extendingukrain'Mat' '' so,/;r.in.'n. S. c'onnected

r ' xu,o"vto-i-iuttiptv -r2r0; u. G. 7 of risttqorl'tzot "ii method N;;il'stsn ;;il.'ema'^ region(Russian) MR36#r626t"'#Jn;;;;;i''souiJtM;;'ootci"s(1e6?)'e80-e841 of theFifth

56. '{el'-sandrov,t- ii",ri,

I

I

" [24, 601 r A' 62 participants)'lyceedings lr:r:tot:1::i". .participants).(Univ. et al (62 l' { er Mariae C,rri.5T.Ateksandrov' r,n,iion'., i)ityii, pp' Ann' univ' Con.ference on.. et"'i' tlro;' iot #t0s62'

4s snoao*ska''"o"n''i+-22 ;;;tr goi/t'x lnn s..t.Tl Mariaecurie-SkroJo*rr.u t44l

53.etenicyn,Ju.E.Univalentfunctionswithoutcommonvaluesina

-=-I

t42

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

contemporary Problems in muttipty connectedregion (Russian)' Conf., Erevan, 1965(Russian)' Theory Anal. Functions. Internat. pp.9_11;MR35#55q7lDokl.NaukSSSR11167,9_ll;MR33#7515}.

59. ffJf$",

in a vatues functionswithoutcommon Ju.E. on univarent

m u t t i p l y c o n n e c t e d d o n t a i n . ( R u s s i a n ) D o k l . A k Soviet a d . N aMath' ukSSSR translation: 167(l 966),9-11;MR 33 #1Yj. tpnglish Dokl. 7(1966),305-3071'122'261 vtithout common valuesin a 60. Alenicyn, lu.'f,. Univaleit functions (Russian) Trudy Mat' Inst' steklov' muttiply connected domaiin". Akad. }iauk SSSR|67(|966), 94(1968) ,4-|8; MR 37 #|57g.[Dokl. of the GeometricTheoryof 9-11; MR 33 #7515},lBook: Problems ' Functions,An:er' Math' Soc' 19691 126l proceedings of itt. Steklov Institute of 61. Alenicyn, Ju. E. problems of the geometric Mathematics,No. 94(1968):Extremal E. Alenicyn.Translatedfrom the theory of irnctions. Edited by Ju. RussianbyA.Yablon,kv;A-,,.Math.Sco.,Providence,R.I. 1969.VI + 167PP'; MR 39 #2963'[44] of areosfor functions which are 62. Alenicyn, Ju. E. Sornetheorerns a n a l y t i c i n f i n i t e l y c o n n e c t e d d o m a i n . D o k l . A k 115-419]; a d . N a u k MR S S Sa8 R209 1a(1913), Math.-Dokladv SZi-sz+. lsoviet (1973), # 2 3 7 2 , # 1 1 4 6 ? . 1 2 7t

? , -r-.a:^{ .,nn!t^v,o uti t' analy-ticfunciions with thecrems for areq Certoin E. Ju. 63. Alenicyn, Mat' Sb' (N'S') 94(136) quasiconformal contin'utation.(Russiani' S S S R2 | 5 ( | 9 7 4 . )|,0 2 5 ( | 9 7 4 ) , 1 1 4 -| 2 5 , 1 6 0 ; D o k l . A k a d . N a u k

1028;MR 5| #3432'lrsl

of the G. V.; et al' Extremal problems 64. Alenicyn, Ju.E.; Kuz*inu, geometrictheor,ofJuticticnsofgcomplex,,ariable.Consultants Rus[Translatedfrom the Bureatr,New york, 1g74, pp. iu-ll7 6l; MR 50 #581' t4l sian. J. SovietMath '2(lg74t' no' aiid .l .Y . The curvaturecJ"leve!citrves 65. Aleksandrov,I. A.; sobole', the of conJormal mappings their orthogonal traiectories in certain 2.26(ig74), 510-516, 574' 135' hatf ptane. (Russian).ukrain. Mat. 571;MR 50 #4919 starlike schtichtfunctions' J' I'ondon 66. Anderso,l, J. M. A note on M a t h . S o c . 4 0 ( 1 9 6 5 ) , 7 1 3 - 7 1 8 ; M R 3 2 # 2 0 3 ' 1 6 ' 6 2 1 theorem' t'orollarl' of Teichmuller's 67. Antonjuk, G. K. A certain (Russian).Proc.Sixthlnteruniv.Sci.Conf.ofth eFarEaston Differential and Integral EquaPhysics and Mathematics, Vol. 3; Gos. Ped. Inst. Khabarovsk, ticns. (Russian),pp . |4-|g.Habarovsk. 1957;MR 4l #3744't54l , ? r ,.,- -t^...^r-: ^n) Zlotkie. Ttntl' gnd resultof Lewandowsk; certain a on K. . G Antonjuk, 68.

l*

BIBLIOGRAPHY

OF SCHLICHT FUNCTIONS

(PART II)

i43

wicz.(Russian).Trud.Tomsk.Gos.Univ.Ser.Meh..Mat.210(1969)'

in t:':r^;,!,;i"i;']?lr"?:!{"nctions thatareextremat

.r i;"*,1;

m''i'il;ii"il*' the coefficieittproble

Ucen' fr tuu*ot' Gos'Univ'

(Abstract no' 95' January196? ,,'fij*jnR:tii:,':yh,:iii,'{,i,artikerunc,ionsorovd issue f ti-'t"' ' Vol e' ft'f' S' Notices 642-111)'t6, 361 Dokl' T l . A v h a c l i e v , F ' G ' O n s u f f i c i e n 'oU'J' ' ? o ! , !i'LArc^''^ , ' ' ' , i o n s f o(Russian) r t h e u n i vlvlath' alenceofthe so'iet #rs82; 4r solutionsoI inverse ^iuunao'y ftR int:+s8;

Akad.NaulsssR rri(t;;;;i

tic runctio:' oranat; no' rqz0' 11(102)' i;iiri'i;"olln" ,, ?lliH*t'::#,!l; zur"a'il;;ffii"" u..i". vy:*. (Russian)'rzv.

se-! cto ild "''"^;;i:{r:{,ff{.'' Y!;1W ii!"""t ,, i;#li1 intesralrepresentotio'ii'rt'rutr'Z^^"j1r21Ol'581-592;MR44 of univolence #4|g1.lMath.Notes,iiniol,jso.liile"grishtrarrslationJ.t'21 tir'riois problem ona *iiL /i, on Sem'Kraev' G. .74.Avhadiev, . F i*;tti""l3rudv problet;: in inverseboundor,1"tute 50#618'[62'68] t:to'

in nonconvex vvp' 10qniiii Y'1 ri, uiiuarence zadcam' rir^t'iinaitt"rt sy .r5.Avhadiev, i. c. _

domains'(Russiatlii'i*rt'rnru''''"i\(l'l4)'963-971'1180;MRs0

u":Hu.l' '2:^I:,J'i|'ffii'i! #:";' t a'luffi':Y:^:::1",fli ,u maPPIng conformal for the ?93-802.[41 Sufficient-conditions A' L' G'; Aksent'ev' Dokl' Akad' Nauk 77.Avhadiev, F'

of onoty'ii,irrryyoll.^e#i1p univ'renci:e

,,

insur. iple pr inc \'}i;}ii:?:,.n 'SSR f:,{':}li*1,: fiiSl,Pi q"T' etao' Nauk e347i, un',ence'Gi$;;j Dokl'14(19?3)' ficiei'conditions #4288;5;;ilVath' oa 2rr0e7r,rs-22r'nrn31' 71-l 16, ,tn.'(| ,-i, +,5, 9,,

onsufficient results fttndqfttental

TslJ#iH;,ni,i:i;::n;!"fi;:i;i:il';';;"t*"*ianiiJs

onvex ctose-to-c or K]';-":# Izv' vyss' :'i:n (Russian) -. Xll"il#:S:3#:li# 'oii' p'oarc*'' '14' bounda'y to inverse MR3T#424't 3-r0; r-gog,'f,ileir:), ucebn.zaved.nn"r*"rir.u Istanbul (Turkish summary) sl functioHs.

functions

g 1. Ayirtmar, N . on univsrent

i;--*

r44

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

univ. Fen. Fak. Mec. Ser. A28 (1963),9-17; MR 34 #7785.t8l 82. Babenko, K. L A contribution to the theory of the secondvariation of functionals on the clsssS of univalent functions. Soviet Math. MR 45 #3690a.[Zal Dokl. l1(1970),no.4, pp. 1037-1041; of extremalproblemsfor theory the of aspects 8 3 . Babenko, K. I . Some univalentfunctions of classS. SovietMath. Dokl., Vol. 1l(1970)' no. 5, pp. 1141-1144MR 45 #3690b.1241 84. Babenko, K. I. On the structure of the cocfficient-domain for univalentfunctions of c/asss. Soviet Math. Dokl., vol. 1l(1970), MR 45 #3690c.[24] no. 5, pp. 1170-1173: of extremalproblemsfor univalentfunc' theory The K. I . 8 5 . Babcnko, of the SteklovInstituteof Mathematics, tions of classS. Proceedings No. 101 (1972).Translatedfrom the Russianby J. W. Noonan. Amer'.Math. Soc., Providence,R. I., 1975.III + 327 pp.; MR 51 #8397. [441 86. Baernstein,Albert, II. Someextremalproblemsfor univqlentfunc' tions, hormonic measures,and subharmonicfurtctions. Proceedings of the Symposiumon Complex Analysis (Univ. Kent, Canterbury 1973),pp. 11-15.London Math. Soc. LectureNote Ser.,No. 12, cambridge Univ. Press,London, 1974.Wal; MR 52 #59M, #843C, #9207 87. Baernstein,Albert, II. Integral meons, univclent functions ar"d cir139-169.U , 3, 16,U, cular symmetrization.Acta Math. 133(1974), 421 88. Bahtin, O. K. Certain extremttlproblems in conformal mapping. (Russian)Ukrain. Mat. 26(1974),517-522, 574; MR 50 #13490. [34,60] 89. Bahtina, G. P . A certain extremntproblem on the conformal mapp' ing of the unit discoitto nonoverlappingdomains. (Russian)Ukrain' 646-M8, 716; MR 5l #8398.124,261 Mat. Z. 26(1974), 90. Dahtina, G. P. The extremizationof certainfunctionals in ihe problem of nonoverldppingdomains.(Russian)Ukrain. Mat. 2.27(1975), 202-2M,285; MR 5l #8399.124,261 91. Bajpai, P. L. Somercdii of starlikenessunC convexityproblems. Indian Institute cf Technoiogy Kanpur, Kanpur, India. Doctoral Dept. of Mathematics,August 1973.12,6,9,10, ll,12, dissertation, 1 3 ,2 2 , 5 6 , 6 r , 7 2 , 7 3 , 8 2 , 8 5 1 gZ. Bajpar, P. L.; Singh, Prem. The radius of starlikenessof certain MR analyticfunctions. Proc. Amer. Math. Soc. 44(1974),395-402; 49 #fi3}. [6, I U 93. Bajpai, S. K. A note on a classof sturlikefunctions.Indian J. Pure

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l2l g72)'no'5 '750-754:MR 48 #6384'16' Appl. Math' 3(1 analytic of theoremti, certainclasses 'f.p"t, convexity Two K. s. 1973)' Bajpai, ,4. Notitl' A'M'S' 20(Feb' (preliminary functions. 85]

Abr,ru.t ?3T-Eo2' [1] ' nr ^-ctnrl ) 5 . B a j p a i , s . K . T h e o r d e r o f s t a197' r l t k eAbstrari . n e s s o f alzr-8233' - s t a r l i k e P' f u nA-491' cttons. Notices A.l,{.s. 20, e.rgurt [ 11 , 6 9 ] 9 6 . B a j p a i , s . K . A n o t e o n o c l a s s o . f m D7l;eust11Lt^7,4T-P,99' e r o m o r p h i c u n i v a l e n t f[9' u n 851 ctions,,

Amer.Math.so..il,April Notices of norrnaliz a-convexitv gT.Bajpai,S' K ' Inftuen"if 1i2f;Q) ?'the Math' Amer' of ordlerB. Notices ici anorytrc funciri^ edstarrike p A-487't69j Proc' Soc.21,August.197+,elrirLih,fr-B141, for rlarlike-functions' of a-convexiiy gg. Bajpai,s. K: on regions t69l MR 49 #91'78' giil,365-368; of Amer.Math.Soc.44(r certainclasses

subordinationfor gg.Bajpai,S. K.; Dwivedi,S. P . A Math' soc' 2l(1974)'Abstract AmerNotic.s analyticfunctions. 10' 85] 74T-822'fi,pA-5M, [1: 6' oJ a-convexityfor sub' on.regiorts S'J'T Mehiok' n'; 100.Bajpai,"S' A' M' S' 20 August 19'3' of starlikefun'cionr. Notitti classes 691 and Abstract73T-B202'p'A-484' ll2' tie coefficientstructure on T.J.s. Mehrok, K.; s. spiral' Bajpai, rs 101. t"iyo.:cl' c'(z) growth theoremfor t:hieftnctiont irri iotlol (1973)'5-r2; MR 50 like.Publ' Inst' rnrutt''igeoeradXN'S;

r;XT,,L1',l:,'$ehrok' r'J?- 9,,! ":::,'::"":l':#;::::'1,"' toz. sturlike, convex and close-to-convex iirn orrr. iated

function f u n c t i o n s . I n d i a n J . P u 47', r e A85] ppl.rvrutr'.4(19.73),no.1,66-721,MR [4, 5, 6' 10' 16' 48 #478:9. p-valentstarlikei; .s. on the rqdiusof 103. Bajpai,s. K.; ror.nroi, n e s s a i l d p . v a l e n t c o n v e x i t y . R 6' e v . - R12' o , , 14' * u i 431 neMath.PureAppl. ** 50 #4923'14' I l' , 973-976' 19(19?4) of meromorphic ni;, on the ciass Nlehrok,T.J.s.,4 K.; s. lM. Bajpai, .|,43_40.t9l;MR 52 P;['. Math.litrql', no Ann. I. functions. #720

-

^ ^ - . n i - n t n c s o "n f n n a l v t i c f ' u n c -

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"'o R,t l :'';.:::o'f:{,:"#:#': $.t;.lli'*'i'""""u' t"it'llt, 106. Amer' Math' Soc' Proc' ' of ,ri"ilrit function'

starlikeness 11' l2l fufn45 #3687't5' 6' 10' 32(1972),153-160; l0T.Balasubrahmany"*,''Lakshminarasimhan,T.v.onsome

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2rl

108. Baranova, V. A. An estimatefor the coefficient cq of univalent 12 (1972), functions depending on | .r l . (Russian) Mat. Zametki Mn 47 #5245.14, 127-130.IMath Notes l2(r972), 510-512(1923)];

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109. Baronov&,V. A.; Lebedev,N.A. On a lemma o-fG.M' Golozin' (Russian)Zap. Naucn. Sem.Leningrad.Otdel. Mat. Inst. Steklov. MR 5l #10609't68l (LOMI) 44(1974),7-16,186; 110. Baranov?,V . Y . Paramet:ic representationof functions with shtft symmetry. (Russian)Theory of optimal processes(Russian), pp' 54-63.Akad. Nruk Ukrain. SSR Inst. Kibernet., Kiev, 1972;MR

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ll1. Barnard, Roger W. On bounded univalentfunctions whoseronges containafixed disk.Notices.A.M.S., vol. 19, no. l, issueno' 135, Januarylg72 (Abstract691-30-7),p. A-112' [6' l6] 113. Barnard, R. w. on a coefficient:nequalityfor starl,kefunctions. MR 50 #4924.[5, 6, 41, Proc. Amer. Math. Scc.47(1975),429-430; 5 4 ,7 5 , 7 9 1 ll4. Barnard, R. w. on the radius of starlikeness of Qfi' .for "f uni,talenf.Proc. Amer. Math. Soc.53 (l 975),385-390.[6, I U; MR 52 #3497. l15. Barnard, R.W. A variationaltechniquefor boundedsrarlikefunct i o n s .c a n a d . J . M a t h . 2 7 ( 1 9 7 5 ) , 3 3 7 - 3 4 7M; R 5 l # 8 3 9 3 . 1 6 , 2 2 ,

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115. Barnard, R.W . On the radius of univalenceof the imagesof linear cpe;"atorson the classs. Notices Amer. Math. soc. 23, Janrtary '/31-30-16,p. .\-101. 113,471 1976,Abstract ll7. Barnard, R. w.; Lewis, J. L . A counterexampleto the two thirds conjecture. Proc. Amer. Math.Soc. 4l(l 973), 525-529: MR 48 #4290.[6, 12, 16, l9l I 18. BarnarJ, Rogcr; Lewis, John L. Coefficient boundsfor some ,325-331.[6' of starlikefutictions. Pacific J Math.56(1975) clc,sses 361;MR 52 #730 of 119. Barr, Alv;,n F. The radit-tsof univalence of certain classes analyticfunctions. Nofices,A.M.S., vol. 18, no. 7, issueno' 133' Nuvembe; l97l (Abstract689-816),p. 1056' [6, l1' 43]

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p p . ; M R 4 9 # 9 1 9 6[.l ' 3 U (tngteichung fiir quasikon' 136. Becker,lorrr.rr. iulr' ttnl Golutinsche '!31(1973)' 177schlichfeFunktionen'Math' Z' form fortsetzbare 182;MR 49 #7440.U, 9, 531 which . Behan,D. F. Constantmuttiplesof a holomorphicfunction 137 A'tvi'S' Notices' ore subordinateto that finction' Abstract: 1 7 ( 1 9 7 0P) P , .1 8 6 - 1 8 7U' l OfLa; Sla'lkowska,Janina' A certain area I 38. Beresniervicz-Rajca, ZeszytyNauk' theorem.(Polish.Russiinand Englishsummaries)' 127-l4l; MR 5l Politech. slask. Mat.-Fiz. zeszfi 24(1974), #10608. [34,861 of subordinatefunctions. Duke r39. Bernardi,s. D. speciat crasses [1' l0' 20' 47' 64' 851 55-67;MR 32 #585?'' Math. J. 33(1966), courant In140. Bernardi,s. D. Bibiiographyof schtichtfunctions' Sciences,New York University' Tech' stitute of tv{athematical + l57pp'; MR 34 ReportNo. NRM1-019,IMM35I(1966)IX ? -t, ^-^^ -F-^ra Trans. univalent functions. siarrike and l4l. Bernardi,s. D. convex 38 MR pp.429-46; Amer. Math. Soc.,vol. 135,January,|969, 6, l 0 ' 8 5 1 #1243.12,5 of certainanalyticfunc' l4z. Bernardi,S. D. The,idiu, of univalence MR 40 #4433' tions.Proc. Amer. Math. soc. 24(1970),312-318; 1 2 , 56 , , 1 0 , 1 2 , 4 3 , 7 3 , 8 28' 5 I of the uni.tdisk'NoticesA' 143.Bernardi,s. D. univalentconvexmaps M.S.,vol.|7,no.Z,issueno.!20,Feb.1970(Abstract70T.B54)' p . 4 4 1 . 1 4 , 5 , 61, 0 ,! 9 , 3 8 '5 4 1 of the unit circle' I I ' . Bernardi, s. D. (Jnivalentconvex inaps 144 no' l2l, April' 1970 Notices,A. M. S., vo!. 17, no. 3, isiue 64] (Abstract70T-B77)p' 566' [4' 5' 6' 10' 19' 38' unit circle' III ' the of mops 145. Bernardi,s. D. (Jnivalenteonvex |9i| (.Abstracf' nc. 130,.iung A. M. S.,vol. 18,no.4, issue Notices, 7 1 T - t s 1 1 3P) ,. 6 4 0 '1 4 ,5 , 6 ' l 0 ' 1 9 ' 3 8 ' 6 4 1 andstsrlikenessof certain 146.Bernardi,s. D. Theradiusof univalence Soc.' vol' 20' of anatyticfunctioni. Nctices,Amer. Math. classes I I , 43] no. 3, April tgll iAbrtru.t 73T-B135, A-332).[6, #2849. l44l

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NewYork, rg74'vI + 180pp' l44l;MR 52l!944 of close-to' ponnnner€rike,Ch. C;i the coefficients

Zgl. Clunie, J.; cgnvexunivolent.firrctions.J.LondonMath.Soc.4l(1966),161_ 38' 54] t65;MR 32#7734[4, 5, 6' 22' 30' 36'

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71',731 35(1g72),iol-zto; MR 45 #5335'[5' 1z', with bounded Functions R. B.; ziegler,Michaei

2g3.coonce, Harry PuresAppl' 19(1974)' Mocanu variation Revl RoumaineMath' 1 0 9 3 - 1 t 0 4 ; M R 5 0 l - 1 0 2-w. 2 4 ' 1 4 ' 6 ' 1 0 ' 2 3 ' 4 3 ' 6variability 9 ' 7 0 ' 7 1 ''for 76'831 c' Domains of 294.cowling, v. F.; Royster, Proc.Amer' Math' Soc' 19' no' 4' August UnivalentPolynomiais. MR 37 #2976'14'321 1968,PP. 767-772; regularand Zg5.Craig,C.; Macintyre,A. J . tnequilittesfor functions boundedinacircle.PacificJ.Math.20(1967),M9-454;MR34 #7806.122,49, 6ll

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s7:t

lf,'

"

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functi onal s

in a

(Polish' zg|.Czubak,Jerzy.Extremgllimitfunctionsforcertotn o;''n'o' the identity' thst functions Mat' Przvrod' fomily of univatey! *""\ yti;'. L,6dLk.Nauki gzesiv;r summar French ' 122'6rl 3-30; MR 48 #11467 Ser.II zeszvt3g(Mai'i'tiqll)' of somefamilies of of radi:' the On ' J 2g8.Czubak, "::::,i'on'ia7"ss in the unit.disc'(Polishand k-symmetric holomorphicfunctions 208 Mat' Nauk,potitectr. L6d2. No' Zeszyiv summaries) Russian

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300f?l:.:i?tti:undnrv,ot:,::1.,,r^r-,!o','!"':':t:::ii::,T!,! (serbo-croatian'French of somec,lasslsof functio'ns. 31 resultant st-55; MR 15(1963)' Bull. Soc.Math. Phys.-itttit summary)

ti,T) o,::::'!,'fi,! properti,,, :'i 1 ,uo*urv) rt;:it" 1. Hii"1,;i (1967),169-l'tz; 30 ."!,', r(ir*li: 4(r9) tvtat.'T.rnir. French croatian.

du timites desvaterus d'existence theoremes MR 51 302.H#Jtf,t.'n|lr?)r^ Balkanica4(1914)'111-114; produit d,Hadamr;;.uatt,.

tJlltto rheschwarz r Lti'ltl 303 !::':,o^','ior(i{X{i{{'lil;;ttn'

CarusMathematicalMonograpr'',N".|7.T|:MuthematicalAs. s o c i a t i o n o f A m e r l t u ' g u f f u l o ' N of ' V ' the ' l g ' lGrunski'-Nehari 4 ' X - I + 2 2 8 p p 'Inetal \i-'Gener(rriz.atiiioir' D. pp' Temple, t53l 304. De Mav 18' 197o'99 stanfordUniv. (Disser;;i"t; q,tutities. bounded for w. on coefficientinequarritiesI' vol' 469 A) 305. De Tempre.Duane ecadl Sci' renn' (Ser' univalentfunctioni. enn. 22' 301 In(1970),l-20; MR 43 #5020'tl9' the Grunskv-Nehari .Tempre, Grnr-rouzott'onr'of . w Duan" 306. De vol' 44(1971/12)'93-120; Arch. iational Mech..A,'t'ur', equalities. 30' l-3' S+l o't fufn+q #556'ilg' 27' 24' for c subclass inrqualities w.-bruns*y-Nettori D. 307. De Tempre, b o u n d e d u n i v a l e n t f u n c t i o n ' r ,531 uns.Amer.Mattr.Soc.l59(1971I),

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'The 225;MR 46#s60a't221

for application of electro-modeling cir324.DunduEenko,L. E. a rinesin convexmappingof riier of curvature trte estimating 33 Mat. z 7(1966),270-284;MR cular ring. (Russian)Sibirsk.

subctass fo-racertain formuta L' E' on ttieinversion 3zs.ir\1i5;Jl;tl3] oftypicallyrealfunctions.(Russian)Ukrain.Mat.Z|8(t966)'no.

U3' 231 3, 107-tti; MR 34#2851' of regurarfunctions L. E. on certain crasses 326.Dundudenko, u n i v a l e n t i n o i , l e l t i p s e . ( R u - s s i ' a p33 ] r#5853' z v . y v lt6' ' . U10' c e571 bn.Zaved MR MatematikaI g66,no'Z(Sfl' S8-61; doublyspirolin o ring' (Rusnedhr E. functjgls L. 32i . DunduEenko, MR 36 #3969'[6' 48] 1272-1283; sian)Sibirsk.Mat. 2.v,o967), of analytic{:t:ctio:t-i:,:" classes 3zg.Dundu6enko,L. E. oi some and Englishsummaries) Russian region (Ukrainian' n-connected N{R35 RSRSer.A 1967,109-112; Naul-ukrain. Akad. Dopovidi #3s7. oJfunctionsthatareanalytic L. O . On a certainclass 32g. DunduEenko, andRussian circutardomain(ukr;inian. English irtan n-connected summaries)DopovrdiAkad.NautUkrain.RSRSerA1-972' 398-400 , 475; lviR 46 #5598' t60l Trans. for startikefunctions. coniecture p. Marx the on L. Duren, 330. M R 3 1 . t I , 6 , 1 2 ,1 6 l A m e r .M a t h .S o c .u g ( 1 9 6 5 )3, 3 1 - 3 3 i ; me;omorphicschtichtfunctions' 531 331. Duren, peter L. ciliirienis -o! teq-172;MR 42/16212'19'25' proc.Arner.Math.s;;. zg(lglt), of univalentfunctions of coefficien;ts 332.Drifeo,Perer\,. Estimat;o'n J. London Matl'' soc' (2) 8 theoreiremainder Tauberion by a sr #877' ls4' 621 Arrrer' 0n4;,27g-2E2;MR of univateitfunctions' Notices' 333. Duren, P. L. Coefficients p' A-98' [9' 25' irt-:o-4' Math.soc.23,lunuurv lg76,Absi;ract tii homeo' o' scht'tarzianderivativesand L.; 3q4.lt;rii, .Lehto' morphicextensio,,.R,,n.Acad.Sci.Fenn.(SeriesA)I,vol. 3U mOgiol, l-11; MR 43 #7610'[4' - ? 3 5 . D u r e n , P e t e r t - . ; t u c r , a u g h l iJ., n , R\9(1972), enate.T w o3,- spp t i't m appingsandthe 267-273; tro' Marx conjectur".tutrchiglnvruth. M R 4 6 # 3 7 6 2[.] , 6 , 1 6 ' 1 9 ]

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681 #6605.125,27, 42,..54, Funktionen.II.(czechsumnrary) scittichte uber . 33g. Dvorik, oldrich MR 40 #5846'14'42' Mat. 94(1969),146-167,222; casopisPes^r. 45,681 of univatent functionsand genei'al340. Dwivedi,.s.P . certain classes i z a t i o n s o f f u n c t i o n s w i t h b o u n d e d b o u n d a r y r o t a Doctoral tion.IndianlnMathematics; stituteof TechnologyKanpur, Dept. of 1975'[1' 5' 6' 9' l0' 12' 23' 42' 43' 49' 7l ' September dissertation, 7 3 ,i 6 , 7 7 1 extr\maresdansrafamirle 34r. Dziubiriski,I . L,equation desfonction ' Panstwowe et bornbes desfonctions univalentessymdtriques ' 122' pp.; MR 33 #5885 wydawnictwoNaukowe, Lodz, 1960.62 241

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NaukArmjan'SSRSer'Mat'4(1969)'no'4'225-243;MR42 #6206.16,23,36, 631 whoseimagesare 348. Eenigenburg,P . on'a classof analyticfunctions NoticeS'A' M' s'' vol 16' star-shapedJordan domains.(Abstract), 12' 361 n o . l , i s s u en o ' 1 1 1 ,J a n' 1 9 6 9 p' ' 1 9 3 ' [ 6'

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360 fi;Il?;'i

Bieberbach coniec?i'::X'' estimste':::' :;::'n:o' g74)' I 126' 142'541

I' An:-lvse I 1: ture 'Math' Z ' r+Otr iistortiontheorem' ,qhlfors' oi Rem;;i, G. 361.Eke,B. gl-ir4; NiR 35 #6806't62l Math' 19(196'7)' n;eati valentfuncbeha";;; of-arially orr^rir'otic The . G 362.Eke, B. vol ' zot't967)' 147-212; Math.*"ti'"e' tions.Journal o{""rrse MR 36 #533t' [8, 33] , -strrqs' -,-inn proc. Roy. Irish Acad. Secr.A 70, t on note A 363. Eke, B' G '

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m a l m a p s . M i c h i g a n M a t h . J . l 4 ( 1 9 6 7 ) , 7 9 - 8 ;gtobar 2 univalence Jacobianmratrixand The H. Nikaido, D.; Gare, 4r7. 8l-93. Annalen 159(1965), of mappings.Mathemalisch. in the theoremfor functions bounded 418. Gal'peritr,I. M. A distortion l, 107-t09;MR ukrain. Mat. Z. 18(1966),no' unit disc.(Russian) 33 #2807. 122, 6ll of o-fseveralof the first coefficients 4lg. Gal,perir, I. M. on estimates Teor' in the unit disc' the Taylor serles of functions -unit'qlent 3s zen'Vyp' 2(1966)'75-78';MR Funkcii Funkcional.Anai. i Prolo

4zo.tlJl;ltj',

fiir die lasse\-spiratischer M. ,uberdeckungssatz

F u n k t i o n e n . ( R o m a n i a n s u m m a r y ) g u t48 t . I#2360' nst.Po litehnlasi(N.S.) t6l -Ine'quarities t-2'sect' l' 59-60;MR l8(22)(1g72),fasc' comnt' p. for the fifth coefficieni' rzr. Garabedian, R. 42' 531 MR 36 #5326'124, pure Appl. Math. rqiift6), 199-214; bearing of Grunsky'sinequalities p. R. ,4n extension -97; 4zz. Garabedian, ' J ' D'a"alyseMath' 18(i967)'8l coniecture on theBieberbach M R 3 7 # 1 5 8.31 2 4 ,4 2 , 5 3 '5 4 1

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lel certainfunciionals in a 430. Giec, T. The timit extremalfunctions for that are neorly the rdentity' zeszyly family of univalentfunctions II Zeszyt 20 Nauk. univ. L6d:k. Nauki Mat. Przyroc' Ser' . |22, 29| Matematyka(1966),161_t83;MR 50 #134q1 rG) - F[8o(D)' 431. Giec, Tadeusz' The range of the functional French summary) Zeszyy Ailr;tOlf in the classSlur . Folish. lI zeszyt29(1968)' Nauk univ . L6d2k. Nauki Mat. Pryzyrod' ser' 49-62;MR 40 #332.[22,30, 49, 6ll of bounded 432. Giec, Tadeusz. certain extre:matproblems in thelamily summary) zeszyty symmetric schlicht functions. (Polish. French Nauk.Univ.L6d2k.Naukiat.Przyrod.Ser.IIZeszyi34(1969}' 23-71M ; R 4 l # 1 9 8 '51 2 2 , 2 4 , 4 9 ' 6 l l ir the 433. Giec, Tadeusz. Estimition of thefunctional lz's'(Q)/s?Q)f Univ L6d2k' c/ass Sf . (Polish. French summary) Zeszyty Nauk' MR 48 43-51; (1911), Nauki traai.Przyrod.Ser.llZesz.yt 39 Mat' # 8 7 7 0 1. 2 2 , 4 9 , 6 1 l l of univalent 431. Giec, T. on some extremat probtems in the family Polon' sci' Ser' bounded and symmetricalfunctions. Bull. Acad. pp. 137-lM; MR 46 Sci. Math. Astronom.PhVi.,20(1972),no.2, #7501.122,24, 6lll

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przyrod.Ser.rrzeszv, func' of univarent partiatsumiof a crass curie436.Goel,RamMurti. on the Mariae ult-"' summaries;itttt' tions. (polish and Russian [4' 5'20' MR 41#373s' Seci.A leii; i),,tt-n(r6zo); sklodowska

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f:::':nl-!!oi3,!:"i:r"t"{ir!?' ofuniva':.'' R.M. A ctass 44a.S#] Arch' wisk' (3) 15(1967)' unit disc.Nieuw

realpar, in ii, positive 1 2 '1 8 ' 1 g ' 7 4 ' 7 5 ' 8 Z l 5 5 " 6 ?M; R 3 6 # 5 3 2 21"2 '5 ' a certoin clossof meromor' 2ElMl. Goel,R. M. Radius i7'ro,rrexill,of I'iath' Debrecen14(1967)' phicallystarlike\rnriior,.s.Publ. 284;MR 36 #5323'19' l2l M z . G o e l , R . M . o n K - f o t d s y m m - e t r39 i c c#4370' l o s e -[5' t o .12' con v e49' x f u74]l nctions. 2A' MR ll-u; i' oc' 18(1967), Ganita Russian functions.(Loose of close-to.convex M3, GoeI,R. M. A class 104-115;MR 37 Math. 1E(93X1968), czechoslovlak summary)

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functions' M5. Goel,R. M ' The'oo-gif"i:?{ 541 #3746' 123' ,25-2'7;MR 4l I l(1969) funct,' nivclentlunctions "A 'lott of univdlent to: corrisr'n-dum NI. R. Goel, " Nieuw M6. reailpart in tke-unit disc' positive hlave derivatives whose ilil 42 #483'12'5'12' 18' t9'74', Arch.wisk. (3)lstigio)' 80-8tt with starshapedimages' M. on a crassof functions 44j.ff;.ilt.. 34-38;MR 41 #M9' [6' 11' 20t951 llsiol. J. tutattl. czcckosiovak 201 Publ' Math' satisfyinsReVQ).1:).' o' on . M functions R. 44E.Goel, D e b r e c e n l 8 ( 1 9 7 1 ) , 1 1 1 - 1 . . 7 ( | gand 7 2 ) starlikeness ; r " r n + o # 7for 4 9 certain 4.12,20,43,72]t of conuixtty The'rsdius M' R" Goe!, Mg. 'yith jtxed secondcoelficienls.Ann. analytic funct;cns of classes

(PART IIT BTBLIOGRAP-IiYOF SCIILICHT FTT}.]CTTONS

IlI

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#73r

qnd convexof order a' J' London 457.Goel, R. M . Functionsstarlike } l;R 5 | # 3 4 | 4 .[ 6 , 1 0 , 1 1 ] M a t h . S o c .( 2 ) 9 ( l 9 7 4 / 7 5 ) , 1 2 8 - 1 3 0 4 5 8 . G o e I , R . M . o n a c l a ' s s o f , a nj a ustral.tviath.Soc. t l yr at ircqf tu' n[ c6t' i1o1n's3.6J '. A 4 5 ' 6 3 '6 7 ' 6 8 ] g l s ) , p a r t M R 1 , 4 6 5 3 ; 20(l a classof storlike 45g. Goel, R. I\{.; Singh, Y. coefficient estimatesfor Appl. Math. 3(1972),no. 6, 1118_1130; functions.Indian J. Pure MR 50 #10211.12,6, 16, 21, 36, 631 of certain analytic 460. Goel, R. M.; Singh, Y. On rartii of univalence Appl. Math. 4(1973), 402_42|;MR 5l functions. Indian J. Pure 1 i 8 7 51. 2 ,5 , 6 , 1 0 , 1l , 1 2 , 4 3 , 7 3 , 8 2 1 junctions with quasiconformal 461. Gijktiirk , Z. Estimatesfor univalent pp. Ann. Acad. Sci. Fenn. Ser A I No. 589(1974),2| extensions. 462.Goldberg,J.L.Boundsonthederivativesofpositivefunctions. zli SIAM Rev. 8(1966),343-345;MR 35 #381'12' of funcderivqtives the on 463. Goldberg,J. L.; ullman, J . L. A note vol ' 14' S" M' in a half-plane.(Abstract),Notices'A' tions poiittrve no.2,issueno.96'February'1967'p'279'l2l o'f a complex 464. Goluzin, G. M. Ceometric:altheory of functions Moscow' 1966'628 pp' variable(secondedition). Izdat. "Nauka",

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1

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BIBI,IOGRAPHYoFSCHLICHTFUNCTIONS(PARTIDtT3

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Fr----

114

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Ser. Meh.-Mat. 200(1968),62-70;MR 4l #2024.[39' 541 492. Gopengauz, B. E. certain theorems on functions whose divided Gus' difference is different from zero. (Russian) Trudy Tomsk' univ. ser. Meh.-Mat. 200(1968),3l-42; MR 4l #2023.t39l positive real 4g3. Gopengauz,B . E. Functionswhosenth derivativehas part. (Russian)Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat' 240 (1968),43-61;MR 4l #2018.[2, 19,54, 68] positive 4g4. Gopengauz,B .E. Someremarkson functicns thqt have a Univ' Gos. Tomsk. rea!port of the n-th derivative.(Russian)Trudy 9-17; MR 43 #5037.12,7ll Ser.Meh.-Mat.210(1969), deriv4g5. Gopengauz,B. E. A certaingeneralizationof the schwarzian ative and its opplication. (Russian) Mat. Zametki l0(1971)' 229-238;MR M #5464(Englishtransl. Math. Notes l0(1971), 5595 6 4 .[ 4 , 3 l ] uni496. Gorjainov,V. V. A rotation theorem in the cla,ssof bounded oo' 5, 633-640' valentfunctions. (Russian)Mat. Zametki 18(1975),

lz2, 6ll

in 4g7. GorjainoV,V. V.; Gutljans'kii, V. Ja. The radius of starlikeness conformal mapping. (ukrainian. English and Russiansummaries)' l4R DopovidiAkad. Nauk Ukrain. RsR SerA 1974,100-102,187; 4 9 # 9 1 8 1[.l 1 , 2 2 1 points in 498. G6rski, J. Sotmeappticationsof the method of extremal the theory o,f analyticfunctions of one complex variaore. colloq' Math.ll(l96-1/64),151-156;MR30#4917'124'541 univalent 4gg. G6rski, J. some shorp estimations ctf coefficients of #3591. 3l MR t54l 199-207; functions. J. AnalyseMath. l4(1965), to needed points method 500. G6rski, J. Application of the extremal Ann. some variatioial problems in the theory of scl'tlichtfunctions. Polon. Math. l7(1965),t4t-t45; MR 32 #5859.124,54'881 of the c/assS' 501. G6rski. Jerzy.A sharp esti,nationof os in a subclass 27-29; zeszytyNauk uriiv. Jagieiio.Prace Mat. zeszyt l1(1966), MR 44 #2921.t54l Ann' Univ' 502. G6rski, J. A certainminimurnprobleni in the classS' 1969/ Mariae Curie-sklodowska,Scct. A, Vols. 22/23/24(1968/ 1970),pp. 73-77(1972);MR 49 #10872'l54l in the clqsss' 503. G6rsk!, J. Locai ineqtnlitiesJ'or scme functicnals [54] Ann. Poion. Ivlath.24(tg7\), Fasc.2,219-224lvIR 14 116949' in a5 Re and aa RE 504. G6rski, Jerzy.Some lotcalproperties of Re as, Katowice-eh-Prace the classS. (Polish srrmrniuY)Univ. 514516iu'r Mat. 2(1972),19-24;MR 46 #7496' l54l s. (Polish 505. G6rski, J. Local inequalitiesof coefficients in the class

(PART II) SCHLICHT |UNCTIONS BIBLIOGRAPHY OF

175

Summary)Univ.SlaskiwKatowicach.PraceMat.4(|973),23_26;

es',',#i{::r'"{:::I;'ff,:' r' r :?::sharp r"J lvfR 35 X*,fi,ti:tJ;ll-] 506. tutotrt.Mech'-ritr966)' 571-582: univalentfunctions.l.

-{"1, ffi%Tll;; MR 42 #477',1 .ii,li;i'ii;t 461; 5cT r}1g;*l' tlg' 22'ni, tLiil"gt.Ji,247-2'5i' z. . ""^tl'I;'}'ir:TI Math Bull' functions. analysis' H. crrvaturr-oni complex wu, MR 44 #473 50g. Greene,n. i., .rtri;;t), iMs-rMg. t35h soc not Amer.Math. lunctionsthat do of univalen-t iiriirir*ts The z. A. 50g. Grinspao, -;' (nu"iun)'Mat' Zametki11 and w it'i' of pair essumeony transi.:Math Notes||(|972), qs n/J,l @nglistr (|972),yt[;MP.

t!1Y1"' y'yr3(Igtz),1'iq-s-tist' MR 48#6403 1199; i':;;,';^ii#:Xi 510'.;1ll;11'1''|' ;i,n:{' i' : :::,:{,f Z. y"i. Sibirsk. 't421 (1973)] (Russian) 793-801 ilii-gl2)' transl.:siu.rianr.n"trr.l. principleto the [Enelish of the are.o opplication rni z. A. _ 609-618 5l I . Grinspan, zametr\11(1972)' fui[tions -n'r"t 8?l 86' Bieberbuch-Eilentrrs 34', ',

1i(letzi,-z'ir-311yyiru!1uY:.:27 closs []{ath.Notes Certainestinntesin the

5tZ. Grinipa^,A . Z.if"fJ"r"lyi^,2,^D. offuncrionsthatdonottakeanypairofvaiue'*.?nd..|.1.(Russian. univ' No' 19 Mat' Meh' Leningrai. -ia-l+'-tsi; v.ruril. Englishsummary) [26'3l' 34'87] r"rn49 13110' ot'g;t' Vvp' (R'ssian) Astronom' oi onot4tlr.,functicns' ,to* c'ertain a on 491 513. Gromov&, L.L. MRll iqz'tl'u9',23',4r', 11^0-113; itrqojt, vyp. sb. that Mat. volz. domains lie ryon-ouerlapping e' N' r-tit;t;' Univ' 24 514. Gromov3,L'r-'; ,rr**uryi v.unit Leningrad' Fnglirt, (Russian. q disk in ;;' it' 7-r2;lurn4r #8646'1261 (1e6e;; for nonover' N' A'-Area theorems itUtatu' L'; L' 515. Gromova' '126' lappingfinitetyconnectedregicn,.tt.(Russian.Englishsunrmary) ;;.'i ,l8-29;MR 41#8647 uniu.25(iqzo;, vestnikLeningruo.

ft analyti: yti : Junc' of anal .- rr /-tu certain nn.' l ,i n cl nssesof classes zluz\n,v^ L.; d,L. j;;:i16; }. ln u 1'23' 516.Gromov MR 33#42s5' 3(re65;, vrp. si. Mat. tions.Volz. 2 7 ,3 4 1

t' I t t::'^'":::'if::J:;:::;!i"o s17'8lo*ouu'L' L'; zvbina' pea. Inst. ucen. Zap. Vyp. 46 co,. functions.(Russi""l,su,uioy. diein Gebieten' von Abbitduns g*:[f, z::i:'f"ri'= f;'x] 685s18 Math' Anal' Appl' 34(1971)' J. einerRichtunst o*-;, srnd. ?01;MR 43 #7605'UOl

b-.-

176

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

Spacemethod in the theory of 5 1 9 .Grunsky, H.; Jenkins,I, A Hitbert proceedingsof the Symposium on- Complex schlicht functions. pp' 75-79' London Math' Analysis(Univ. Kent, Canterbury1973)' Univ. Press,London, Soc. LectureNote Ser., No. 12, Cambridge

re74.t44l

t

the curvatureo'f levelcurvesand 520.Gudz', L.A. Shorpboundsfor theirorthogonaltrajectoriesinclassesofalmostconvexfunctions. Dopovidi Akad' (ukrainian. English and Russiansummaries)' NaukLlkrain.RSRAlgl4'4g4-4gg'573:MR5l#3415'[5'35] functions' 521.Gupta, R. s. on meromornhiclilcularly-symmetric G a n i t a r g ( r g o z ) , t r o . 2 , . 3 t - 3 . 8 ; M R 3 9 # 4 3 7 1 .of t 9o, 1crass 3 , 2 5of, 4 9 | starrikeness univarence.and of Radius s. 522.Gupta, R. analyticfunctions.J.Austral.Math.Soc.14(1972),Partl,1-8; MR 47 #5239.12,11,22,13,567 with positivereal 523.Gupta,R. S. An extrematpiobi* f?' functions part.Proc.Amer.Math.Soc.33(|972),455_462;MR45/2|67; MR 48 #4323.12,561 of analyticfunctions' J' Indian 524.Gupta, R. s. on certain classes Math.Soc.36(1972),fg-gg;MR47#7015't5'9'16'N'41'45'56' 63,67,15,78,791 of convexsum cf univalentfunc525.Gupti",R. S. Radiusof cortvexiry vol' 19,no, . l-4, 1972,39-42;MR 48 Math' Debrecen' tions.Publ. #2361.16,29,35,681 lunctions' of convexityof a classoJ'univulent 526.Gupta,n. s. Radius #5389. 48 [5, 6, 10, MR J. IndianMath. Soc. 36(|972),29|_296; 12, 821 of univalentfuncitons' Rev' Mat' 527.Gupta,R. s. on the integrals [6' 11' l2' 85] yR 50 #13480. (4)34(l974;),iog-zis; Hisp.-Amer. valuesof certainfunctionalssnd 52g.Gutljanskii,v. Ja. The'rangeof thepropertiesoftevetlinesonclassesofschtichtfunctions.(Rus71-87; 200(1968)' sian)TrudyTonnsk.Gos.Univ. ser' Meh'-lvlat' M R 4 l # 3 7 3 7 . 1 6 , 2 9 , 3658, 1 cf univarentfuncparametricrepresentation 52g.Gutrjanskii,v. Ja. 750-753;MR Dokl. Akad. Nauk sssR 194(1970)' tions.(Russian) t68l 1273-127.61' 42 #6201iSoui.tMath. Dokl. 11(19?0), of univalent class the of 530. Gutljanskii,V. Ja. The stratif;,o,,on analyticfunction.s.(Russian)Dokl.Akad.NaukSSSR196(1971)' 498-501;MR42ll7877.[SovietMath.Dokl.l2(197|),155-159}.

l24l theorem in a classof schlicht 531. Gutljanskii, V. Ja. The rotation (Russian)' Mat' Zametki 1C(1971)'239P-sYmmetricfunctions.

FUNCTIONS (PART II) BIBLIOCRAPi{Y OF SCHLICHT

111

242;MR45#sz|[Englishtransl.:Math.Notesl0(1971),565_566]. [49,681 parame*ic representations 532.Gutljanskii,v. Ja. Integro-differ,lltiarEnglishand Russiansumand variations!forntulie. (Ukrainian' Ser'A 1973'781-783' DopovidiAkad.Naukukrain' RSR maries). 859;MR 48 #8778'1241 of distortiongnd on theorems V ,.A. Scepetev, Ja.; V. 533. Gutljanskii, univarent functions.(Russian) rotationon the crassioromorphic S i b i r s k . l . . { a t . Z . 1 4 ( 1 9 7 3 ) , 8 6 7 - 8 7 2 ' 9 1 1 ;crea M P ' 4 9 # 5 6for 0't581 v . A. A generaiizeJ theorem s..p.irV, Ja.; v. Gutljanskii, 534. mappings.(Russian)'Dokl' o certoinclassof q-qiiri;conformat A k a d . N a u k . S S S R 2 : l 8 ( | g 7 q , 5 0 9 - 5 . 1 2 ; MoJ R5|#3434.|27| in thefamily schlichtfunc' estimates certain Eugeniusz. 535. Guz, (Polish' French summary) tionssatisfyingduxitiiary conditions' Przyrod'ser' rl zeszyt Mat. zeszytyNauk. univ. ioart. Nauki 3l-47; MR 39 #5783'[9' 58' 68] 29(1968), functions' oj k-symmetric,un.ivalent 536. Guzek.R. F . The,orlltrrnts ( P o l i s h . E n g l i s h s u r n m a r y ) . Z e s z y t y N(1966)' a u k . I J147-160; n i v . L o MR dzk.Nauki Matematyka przyrod. .ILzesivt20 Ser N{ar. . 122,30,491 50 #2477 uyllesof finitely valentfunctions' 537. Hacdad,David c. Asymptotic 361-368'U4l DukeMath' J' 39(1912)' tintits of locartyfinitery valent A'ngurar 53g. Haddad, David c. 12;MR 48 . 48(1973),107-1 functions.PlcificJ. Math holcmorphic #8802.lr4' 621 under of hyperbolic-curvature 539. Haifawi, M. M. on the behavior ift"d' Circ' Mat' Palermo(2) univalentboundedtransformati('n' 16(1967), 57-63; MR 39 #2964' t35l

tinnc StrrrliaS univarent functions.stucia Sci. theoremsfor Tauberian G. Har6sz, 540. M a t h . H u n g a r ' 4 ( 1 9 6 9 ) ' 4 2 1 - M O ; M R 4 0 # 5 8 4 2of '16'201 pointsof somefamilies univalent 541. Hallenbeck,David J. ;xtreme

functions.Notices,A.M .,u-ol.19,no.1,issueno.135,January' p'. S A-119' [88] lg72(Abstract691-30-32)' pointsof somefamilies extieme and 542. Hallenbeck,D. J. convexhuils Math. Soc. |92(|974),285_ of univalentfunctions.Trans. Amer. 4l' 56' 881 ' U ' 2' 4' 5 '9: -10'12' 16'21' 23'39' 292;MR49 #3103 closefor convex'starlike'ond 543. Hallenbeck,D. J . some'inequalities ' 4llJ' 24 (99) (1974) msppings.czectroslovakMath' to-convex 4 1 5 ;M R 5 0 # 5 8 9 [' 5 ' 6 ' 1 0 ' 6 3 ' 6 4 1 co)iecturefor the convexhulls of 544.Hallenbeck,D. J . On the Marx soc' convex*op"ptnss'Proc' Amer' Math' familiesof starlikeand

17E

BIBLIOGRAPHY OF SCHLICHT FUNCTTONS

4 2 ( 1 9 7 4 ) , 1 3 5 - 1 3M9R ; 4 8 # 4 2 9 3 't l , 6 , l 0 ' 1 2 ' 4 3 ' 8 8 1 of functions defined by 545. Hallenbeck,D. J . Extremepoints of classes MR 50 subordination proc. Amer. Math. Soc. 46(1974),59-64; #10225.[1, 6, 36, 88] points of families 546. Hallenbeck,David J. convex hulls and extreme J' Math ' 57 Pacific of starlike and close-to-convexmoppings. (1975),167-176.U,2,5,6,13,16,23,36,45,75,881;MR52#725 of extremepoint 547. Hallenbeck,D. J.; Livingston,A. E. Applicstions Amer' Math' iheory to classesof muitivalent functions' Notices Soc. 2l(1g74),AbstractT4T-P;221,p' A-5M' U4' 881 of extreme point 548. Hallenbeck, D.: Livingston, A. Applicotion Amer' Math' theory to classeso7 mittivalent functions. Notices p ,. A - 1 0 1 .u , 5 , 1 4 , 7 5 , S o c . 2 3 J, a n u a r y1 9 7 6A, b s t r a c t T 3 l - 3 0 - 1 5 881 chains ond 54g. Hallenbeck, D. J.; Livingston, A. E. Subordination 1976' p-valent functions. Notices Amer. Math. Soc' 23, January Abstract'731-30-6, P. A-99' [1, 4, l4l estimatefor 550. Hallenbeck, D. J.; Livingston, A' E' A coefficient mult;valentfunctions. proc. Amer. Math. Soc' 54(1976),201-2M' ; R 52#8401 [ 1 , 5, 6 , 1 4 , 1 6 , 4 2 , 5 0 , 8 8 ] M and extreme551. Hallenbeck,D. J.; MacGregor'T. H' Subordination ' point theory. Pacific J. Math. 50(l 974),455-468;MR 50 #13481

u , 2 , 3 , 5 , 6 , 1 0 ,1 3 , 2 38, 8 1

by convexfunc552. Hallenbeck,D. J.; Ruscheweyh,S. szborriination MR 51 #10603' tions.Proc.Amer. N{ath.Soc. 52(1975),l9l-i95; [ ] , 4 , 6 , 1 0 ,8 2 ] Mich' 553. Hansen,Lowell J. The Hardy classof a spiral-tikefunction' Math.J.,lS(1971),279-282;MR44/.4211'[6'36'6?l transformations of 554. Hartmann, F. W.; MacGregcr, T. H. Matrix J. AustralianMath' Soc' l8(1974)' 419-435; uni,talentpower series. tvtR 5 ! #10597.[4, 54, 68j of Apollonias' Por555. Haruki, H. On un application of a theorem trrgal.Math. 33(l 974), 167-170;MR 50 #13476.I3ll prob556. Hayman, w. K. Cor:rigendum:Stirvey article-coefficient classes.J. Lonlemsfor unifalent functions and relatedfunction donlviath.Soc.4l(1966),5-{0;MR33#7519.[44] probiems in function theory' The 557. Hayman, W. K. Reseu,rch vII + 56 pp'; Athlone Prcss(univ. of London), London, 1967, MR 36 #159.[16, 44] gops' Colloq' Math' 558. Hayman, W. K. Mean p-valentJunctionswith l 6 ( 1 9 6 7, ) l - 2 1 ; M R 3 5 # 4 3 9 5 '[ 1 4 , 3 3 , 3 9 ]

J

(PART Tt) BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

119

de Les Presses multtvalent'es' 55g.Hayman,walter K. Lesfonctions 40 MR pp'; Que., 1968' 52 l,Universitede Montr6al,ivfontr'eal, . Il4, 441 #5S48 cf meon Hankcl cieterminent 560. Hayman, W. K. On the seconC Soc' (3rO series)'l8 univalentfunctions. Proc. Loqd'''rnMatir' (i968),77-94;MR 36 #2794't33l p-varintfunctionswith mini-gaps.Math' 56r. Hayman,w. K. Mean Nachr. 39(1969),312-324;MR 4C#336't33l multi'"'alent functions' Ac' 562.Hayman,W. K. Tauberiantheoremsfor MR 42 #3270'[seealso]viR48 #505' 269-298; ta N{ath.125(1970), MR 50 #5931.[14, 33, 621 on archproblens in function theory;progress 553. I{ayrnan,w. K. Rese Symthe of Proceedings the previousproblemr; ir* problems' 1973)'pp' CanterbufY' posiumon ComplexAnalysis(Univ' Kent, l2' LondonMath. Soc'LcctureNoteSer.'No' 143-154,155-180. CambridgeUniv.Press,Londor,|g74.Va]tMR52#5944,#8385' #8386 , , n^^:r.inequalilies and local valency. Pacific 564. Hayman, w. K. Differential

J . M a t h . 4 4 ( 1 9 7 3 ) , l l ' l - 1 3 8 ; M R 4 ' 7 # 5 2 4 0 ' t 1 4 1 of theminimummodulus func565. Hayman,w \.; Nicholls,P. J . o Math. Soc. 5(1973)' tionswith given ,orrirrirnrr. Bull. London 2gs-30r;MR 48 #4301'[33] questionctfM. L' cartwright' 566.Hayman,w. K.; Storuick,b. e. A +ig-qzz;MR 47 #5238't621 J. LondonMath. Soc.tz>sttg1z), and meansof the coefficients 567.Haytnan,w. K.; Weitsman,A. on Math. Proc' cambridgePhilos'Soc'77 functionsomittingvalues. ( 1 9 7 5 )1, 1 9 - 1 3 7M; R ' s 0# 1 3 4 9 5[ '3 ' 1 4 ' 6 2 1 Study concerningconformal 568. Heins, Maurice. On o theorentof dedicatedto A' J' mapswith conveximoges.MathematicalEssays Athens,ol^io, 1970; Macintyr€,pp. 17l-t:te. ohio urriv. Press, MR 42 #7878.UOl differentialequations' 569. Heins, Maurice.,4 note on the Lowner 46 #3771l. |24| PacificJ. Math. 39(197|), |73.177;MR 5 T 0 . H e i n s , M . O n a t h e o r e m . o J S t u d y c o n c e r n i n g cMR o n f49 o r#551' malmapswith conveximages.II.Math. Scand.32(1973),245-257; t10l to dowalter;fchober, Glenn. on schtichtmappings 571. Hengartner, 45(1970)' Helv' Math' mainsconvexin oni direction Comment' 791 78' MR 43 #3436'12' lg' 21' 4l' 303-314; closeto siZ. Hengartner,Walter; S.nof.r, Glenn. Analyticfunctions Amer. Math. soc' mappings convex in one direction Proc.

b--.-

1t0

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

28(l97l),519-524;MR43#3437'15,12'41'43'78'791 P,lya-schoenberg 573. Hengartner,w.; Schober,G. E. A remark on the no' 138, June conjecture.Notices,A. M. s., vol. 19, no.4, issue lg72 (Abstract 72T-B150),p' A-5 18 ' [47] des familles de 574. Hengartner, W.; Schober, G. Points extrAmsux sci. Paris 56r. A-B 274(1972), fonctions univalentes.c. R. Acad.

MR 45 #7038't88l A837-A838;

some classesof 575. Hengartner,w.; Schober,G. Extremepoints for univalentfunctions. Trans. Amer. Math. Soc' 185(1973),265-270; M R 4 9 # 5 5 9 .1 4 , 4 1 '8 8 1 of univalentfunc' 576. Hengartner,*.; Schoblr; G. Compoctfamities ' J' 21(1974),205Math tions and their support points. Michigan 2r7 (1975);MR 5l #898.[24' 88] points d'appui des . Hengartner, W.; Schober, G. Propriitds des 57'7 c. R. Acad' Sci Paris famittes compactesdefonctions univolentes. ; 5 l # 8 8 0 't 8 8 l 5 6 r . A . 2 7 9 ( 1 9 7 4 ) , 5 5 1 - 5 5M3R properties of support 578. I{engartn.r, W.; Schober, G. Some new Amer' poin-tsfor compoctfamities of univalentfunctions. Notices p' A-102' [88] Math. Soc. 23, January 1976,Abstract 731-30-18, moxof points counting for function 57g. Herztg, F.; Piranian, G. The proc. Pure Math., vol. ll(1968)' I^r Symposia of modulus. imum 24A-243.[68, 90] 580.Hindma,,h,L.;Volk,B.Schlichtcubesotile|< Math. Monthly, March 1976,'20'l-209'l32l Proc' 581. Holland,F. Somepropertiesof a classof regularfunctions' MR 4l #7084'16,2f,621 Roy. Irish Acad. Sect.A 69, 85-95(1970); relationsfor starlikefunctions'Proc' -A,72(1972), 582. Holland,F. some osymptotic no. 1, pp. 1-16; MR 47 #451' Roy. Irish Acad. sect.

16,621 Proc. 5g3. Holland, Finbarr. on the coefficients of starlike functions. Arner.Math. Soc.33(l g72),463-470:Ir{R 45 #531.[2,6,9,18'23' 25,zil

polynomials with 584. Holland, Finbarr. Some extremumproblemsfor MR 47 positivereal parf. Bull. London Math. Soc. 5(1973),54-58; #8824.12,321 j85. Holland,F. The extremepoints of a classof lunctions with positive 23, 881 reatport Math. Ann. ZOi(tg13),85-88;MR 49 #562' 12,21, slarlike func5g6. Holland, F.; l'homas, D. K. The orea theoremfor tions.J.London Math. Soc.(2)l(1969),127-134;MR 39 #7080'[6' 18, 27, 361 of a starlikefunctions. 5g7. Holland, F.; Thomas, D. K . On the order

A

FU N C TION S(P A R T II) | IBT ,IOGR A P H YOF S C H LIC H T

T81

189-201;MR 43 #343E'[3'6' Trans.Amer. Math' Soc' 158(1971)' 36, 62, 631 5 8 8 . H o l l a n d , F ' ; T w o m e y ' J ' B ' O n c o ftani' e f f i c i eAmer' n t m e slvlath' n s o f c Soc' e r t a i185 n c.f univalentfunctions' suttclos'ses q i r c l g 6 ' 1 2 ' 5 ' ,6 ' , 2 1 ' , 2 2 '3, 0 ' ,6 2 ' ,1 5 1 ( 1 9 7 3 ) ,I 5 1 - 1 6 4 ;M R o"f J 'K' A note on conforntalmappings Kr'owles' O'; C. Horgan, 589. convexmappings.Utrlita,tutu.t'.5(1974),75-78;MR49#9|75.|27, 53, 54'l mapping. Proc. bounclary values o-fo ,schlicht 590. Horn, R. A. on lgz-787; IVIR36 #2i92. i53' 62i Arncr. Marh. Soc...18(t961\, 59l.Hornich,Hans.(]berdieFixpunktederst:hlichterfi:nktionen. (Englishandltalia.nSummaries)Rent.Ist.Mat.Univ.Trieste2

itlzo;, 54-58;MR 42#i989' D.rfferentiargreichung in zusam' Eine . iartrette Hans Hornich, 592.

menhangmetdenschlichtenFunktionen.Monatsh.Math.T6(19,72), l2r-t23; MR 46 #2029' ' estimatesfor univalent PolYnomiols Coefficient D' Horowitz, 593. lgi 5, Abstract 7 20-30-28' P'

NoticesAmer' Math' Soc'' ianuarY A-125.132,121 coefficient estimates for 5g1. Horowitz, David' "1 refinement.for S o c . 5 4 ( 1 9 7 6 )1, 7 0 - 1 7 8 ' Math. univalentfunctio'ns'Proc' Amer'

und Abbitdungen konformer Faktorisieruns Die . lii;i:;,tiluo se5. A r t w e n d u n g e n . M a t . Z . 9 2 ( 1 9 6 6 ) , 9 5 - 1 0 9 ; M RArch' 3 3 # 2 Rational 808.[58,68] variationarlemma' 596. I{uckemann, F. on s.nif)r's MR 33 #1446' 162l Mech. Anal. 22(1966),lib-112; of conformsl irt certain crasses . Huckemann,F . Extremcr erements 5g.7 mappingofanannulus.ActaMath.lls(l96.7),|93-221;MR35 .t t^,uan rr Arnh Ravsriationarremma.II. Arch. Ra' schiffer's on F. 5gg. Huckemann, MR 39 #1652.162l tionatMech.Anal. lliiql"gl ,246.24:; ' J' AnalyseMath' 18 funciions Multivslrn't'ito'iike A. J. 599. Hummel, (1967),iil-160; MR 35 #359'[6',14] 600.Hummel,J.A.Extremalpropertiesofweaklystarlikep-valent functions.Amer.Math.Soc.Trans.rlotr963),544-551;MR36 #5332.[6, 14] of starlikefuttctions' Proc' A' M' 601. Hummel,J. A. Thecoefficients 36',-54\311-3tttMit 40 #M40't4',6', s.22(1969), funcj"' thecoeffi-cient bodyof univarent 602.Hummel,J. A. Boun;; 128andAnalysis36(1970)' for RationatMechanics tions.Archive 134;MR 42 #6213'[6' 36] #3048. t57l

iilt

.

H^-

I82

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

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t8l

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(PART BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

ID

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the elements of E. (Jniversal relstions between Jabotinsky, . 617 4||4|7; MR 35 Math. 17(196o,1, Grunsky,s matrix. J. Analyse # 6 8 0 8 . t5 3 l

,

.

tL^ ot.tnontc

ttl '

6lS.iauotinsty,E.(JniversalrelationsbetweentheelemenlsoJ Grunsky,smatrix.J.enutv,.Math.lT(1966),4114|i;MR'35 #6808.t531 6|9,Jack,I.S-,Functionsstarlikegndconvexofordera.J.London Nlath.Soc.(2)3(l97L),469_474;MR43t'l76l1.[6,10,i|,|2,|6,63, @l t )nt taafnrrnnl mnnninvs. of curvesunder;onformalmappin*s distortion LenSth S. , Jaenisch 620. l2l-i28,.MR 36 #5319.t?' 16' 35,621 Mich. Math. J. 15(1g9g), de sur la dtformatior dars tafamille ;:;''riAo'a^es Jakubo'.*", 62l. inf€ricureo:, p6r, simprea'"r'infiniet borndes fonctions univarentes mentdanslecercleK(-,1).panstwowewydawnictwoNaukowe' 58' 221 L6d2, 1962'43 pp'; MR 34 #326'[9' et p-sym'etriques univorentes 622.Jakubowski,Z. J. sur resfonctions (Russiansummary)Bull' Acad' born'eesdans un cerclounitoire. ' 637-642; polon. Sci. 56r. Sci. Math. Astronom'Phys' 14(1966) M R 3 4 # 6 0 7 1 . 1 2 2 , 4698, 1 At * aAz in the Z. I. rh; miximurnof thefunctional 623.Ja^iubowski, fttmilyofunivolentfunctianwititreatcoefficients.(Polish.French s u m m a r y ) Z e s z y t y N a u k . U n i v . L o d z k .#7502. N a u l c139, i M a541 t.Przyr'od. itqoo), 43-61;MR 50 zeszytzotvtatematyka et desfonctionsunivalentes 624.Jakubowski,Z. J. Sur iescoefficients (Russiansummary) Bull' ' sym'etriquesdans ur cercle uniruire &3Phys'14(1966)' Astronom' Acad.Polon.Sci.Sdr.Sci.Math. 646;MR ?1 #6072'122'30' 39i desfonctions univalentes 625.Jakubowski,Z. J. Sui tescoefficients19(1967)'207-233;MR 35 Math' dansle cercleunit€.Ann. Polon#6814.122,30,39,541 et p-symmetriques 626.Jakubcwski,z. J. LLsfoyctions_univarentes, 119-148; Polon'Math' 20(1968)' borneesdansl, ,rrr"tr-",itr/.Ann' MR 37 #2968.122,241 of Caraft1odoryfunctions' 62'1. Jakubowski,Z . J. O; the coefficients Sci. 56r' sci' Mat' Polon. (Russiansummarvi eutt. Acad. A s t r o n o m ' P h y s ' 1 9 ( 1 9 7 1 ) ' 8 0 5 - 8 0 9 ; Mthe R 4clunie 6 / i 3 7 7method' 0'12'21'561 of 628.Jakubowdki,z. J. on someapplication pp. 21| -zl7; MR 46 #20&' 12,13' Ann. poron.Math.,26(19:12), 21, 41,51, 791 of starlikefunctionsof some 629.Jakubowski,Z. J. on the coefficients c l a s s e s . A n n . P o l o n . M a t h . , 2 6 ( | 9 7 2 ) , N oPhys., . 3 , p p 19(1971)' .305-313[Also: Astronom. Bull. Acad.Polon.sci. 56r.Sci.Math.

b--.

lE4

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

, 7 4 9 7 .[ ] , 6 , 2 1 ' 3 6 ] n o . 9 , p p . 8 1 1 - 8 1 5 1M; R 4 6 # 2 0 3 0 # of thefunctional lf(")(e)l bound upper the On 630. Jakubowski,Z. J. of univalentfunctions. Commeilt. (n - 2,3,. . .) in some classes Math. PraceMat. 17(1973),65-69;MR 48 #2369.[54, 68] 631. Jakubowski, Z. J. On some properties of extremalfunctions o.f MR Carath\odory.Comment.Math. PraceMat. 17(1973),71-80; 48 #52?. [2, 56] 632. Jakubowski, Z. J. On some special class of regular functions. Math. Balkanica4(! 974),299-300. 633. Janczar, B. The structure of boundary functions in the classes quasi-startikeand quosi-convex.functions. Demonstratio Math. 5 (1973),17-27;MR 48 #2362.[6, 10,241 634. Ja;rczar,B. z"-quasi-convexfunctions. (Polish and Russian summaries) ZeszytyNauk. Politech. L6di* No. 186 Mat. no. 5(1974),

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635. Jankovics, Ronalci. Uber Funktionen mit der Eigenschaft Re[ei-lfQ)/z- p\ 5 l # 8 3 9 2 [. 6 , 1 1 , 1 2 , 2 0 1 636. Janowski, W. Sur une certainefamllle de fonctions univalentes. (Russian sunrmar!) Bull. Acad. Polon. Sci. 36r. Sci. Math. Asrronom.Phys. 13(1965),707-713;MR 35 #4386.124,291 637. Jancwski, tN. A certain famity of univalentfunctions. (Polish. Nauk. Llniv. Lodzk. Nauki lvlat. Przyrod. Frenchsummary)Ze,szyty Ser. II Zeszyt20 Matematyka (1966), 3-41; MR 50 #7498. t29l 638. Janowski, W. Sur une certain famille de fonctions univalentes. Ann. Polon. Math. 18(1966),l7l-203; MR 34 #327.124,29,621 639. Janowski, W. On the radius of starlikeness of some families of regulor funciton.". (Loose Russian summar.') Bull. Acad. Polon. Sci. 56r. Sci. Math. Astronom. Phvs. 17(1969),503-508; MR 40 #7438.[6, I l] &O Janowski, W. Extremal problems for a fu,tity cf functions with positive real part arid for scme relsred families. (Loose Russian summary)Bull. Acad. Polon. Sci. 56r. Sci. Math. Astronom. Phys' l7(1969),633-637;MR 4l #1986.12, 12,21, 561 of somefamiliesof &1. Janowski,Witold. On the radiusof starlikeness rcgular tunctions.Comment.Math. PraceMat. l4(1970), 137-149; Mk 42 #6208.[6, 1l] &2. Janowski, W. Extremat probtems -for a family of functions with positive i eal part and for sonrerelatedfamilies. Ann. Polon. Math. 159-177;MR 42 #2005.12,6, I I , 12, 13, 19,21,24' 23(1970/71), 40,411

-_

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II)

1E5

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. , , . - ^ u n - n t coefficient nnoffirient on normalizationin the general A. Jantes Jenkins, &5. Mathematicians(Stockholm' theorem. Proc. Internat. congr' MR 31 tnsi. Mittag.lef|ler,Djurslrolm,1963; |962), pp.347-350. #328iunctions' III' Trans' Bieberbach-Eilenberg on A. J. Jenkins, u6. "241 lvlR3l #5969'I-26,34'861 Amer.Marh.soc. t tq(iqos),lg5.2l5; 17 of Nehari.Proc.Amer' Math' Soc' ,isult a on A. J. Jenkins, &7. 25' 27'29' 541 (1966),62-66;MR 32 #5865'[9' lg' coeffi' certainextremarproblemsfor the 64g. Jenkins,JamesA. on D'analyseMath' l8(1967)'173cientsof univalentfunctions' J' 184;MR 35 #305l'124'541 inequalityconsidered bY Robertson' &g. Jenkins,JamesA' On on June1968,PP.549-550;MR 37 Proc.Amer.Math' Soc'19'no' 3'

#401.18,42, 541 result in conformal mapping' 650. Jenkins, James A. A uniqueness MR 39 #2958'[7,9' 19] proc. Amer. Math. Soc- zzhgog),324-325; ' Proc' on "puirs" of regularfunctions 651. Jenkins,JamesA. A remark A m e r . M a t h . S o c . 3 l ( 1 9 7 2 ' 1 , 1 1 9 - 1 2 1 ; M R 4 5 # 5slit | 9 .mappings' |26,34,86] of certain ripresentation The A. Ju*., 652. Jerrkins. January|g76' Abstract 731-30-21' l.IoticesAmer. Math. Soc. 23,

p. A-102. tglt A remark on P-valentfunc' 653.Jenkins,JamesA';Oikawa'K6taro' 3g'l-4M; MR 45 #3693' U4' tions.J. Austral'Math' Soc' 12(197t)'

of Ahtforsqnd ' on results K6taro oikawa' A'; James 654.?llurtr, 124,331 MR 45 #5332HaymanIll. J. Math.iitr sng,664-671; the coefficient

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660. Kac, I. S. Integral and exponentialrepresentationsof analyticfunctions mapping the upper inlf-plane into itself. (Russian)Problems of Math. Phys. and Theory of Functions,II (Russian),pp. 5l-62. Naukova Dumka, Kiev, 1964;MR 32 #7721-1231 66i . Kaczmarski, J. The least upper bound of a certianfunctional in the famity ofbounded univalentfunctions. (Polish. French summary) ZeszytyNauk. Univ. Lodzk. Nauki Mat. Przyrod. Ser.IlZeszyt20 Matematyka(1966),63-l0l; MR 50 #7505-122,24,291 662. Kaczmarski,J. SurI'equationfQ) - pf(c) dans la classedesfonctions etoilees.(Loose RussianSummary) Bull. Acad. Polon. Sci. 56r. Sci. Math. Astronom. Phys. l5(1967), 455-464;MR 36 #3970. [6,241 663. Kaczmarski, J. Sur I'equation f@ - p"f(c) dans la famille des fonctions univalenteso coefficient,sreels. (Russiansummary) Bull. Acad. Polon. Sci. Ser.Sci. Math. Astronom.Phys. 15 (1967),245251; MR 35 #4387. 124,391 of starlike func664. Kaczmarski, J. On the coefficients of some class'es Polon. Sci. S'er.Sci. tions. (Loose Russiansummary)Bull. Acad. .12,9,251 MR 40 #7437 Math. Asrronom.Phys.l7(l 969),495-501; g-p-N-spiral-starlikeness of the 665. Kaczmarski, J. On the ,oilirts of familyS*(o,},,M)ofspirol-starlikefunctionsinthedisc|z|< (Loose Russiansummary)Bull. Acad. Polon. Sci. 56r. Sci. Math. Astronom. Phys. l8(1970),467-473;MR 42 #4718.[6, I l] 656. Kaczmarski, J. On sotne extremalprobtemsfor certain classesof close-to-starlikefunctions. (Russiansummary) Bull. Acad. Polon. Sci. 56r. Sci. Math. Astroiiom. Phys. 2l(1973), 133-140; MR 47 ffi66j. 12,6, lll 667. Kaczmarski, J. Some radius o,f convexity problems in certainfontity of functions with bounded distortion. Bull. Acad. Polon. Sci. MR 47 #5241.12,l2l 56r. Math. astronom. Phys.2',(1973),27-34; 668. Kaczmarski,J. On the rsdius of convexityfor certain regularfunc' MR 50 tions' comment' Math' PraceMat' !7(1973i14)' -773-383; #2472. 12, l2l 669. Kaczmarski, J. Cn some extremal problem for certain classesof / close-to-starlikefunctions. Comment. Math. Prace Mat. 17 (1973i 74), 385-398;MR 50 #2473.[6, 1l] 67A. Kaliramaner, Suzan. Sur les coefficientsdesfonctions univuienies.

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t35l 683.Kas,janjuk,S.A.;Finogenova'V.G.Theran gesofvaluesof coefficients ond their regions' typically real functions iitn fixed (Russian).Izv.Vyss.Ucebn.Zaved.tutut.*atika1968.no.4(71)' N-47; MR 37 #2977' U3 ' 291 with G' I' A property of functions 684. Kas,janjuk, S. A.; Tiacuk, positiverealpart.(Russian)Teor.FunkciiFunkcionalAnal.i

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Prilozen.Vyp. I(1965),224-227;MR 34 #4508.[2, 39] 685. Kayser, Hans-Ji.irgen.Uber Abschatzungsproblemebei gewissen holomorphenAbbildungen.Bonn. Math. Schr. No. 49(1967),VIII + 55 pp.; MR 47 #452.[l9, 54] 686. Keogh, F. R. A strengthenedform of the f, theoremfor starlike univslent functions. Mathematical Essays Dedicated to A. J. Macintyre, pp. 201-211.Ohio Univ. Press,Athens, Ohio, 1970; M R 4 3 # 4 9 6 .n , 6 , l 9 l 687. Keogh, F. R. A sttbordinateproperty o"f univalentfunctions. Bull. ; R 4 5 # 2 1 5 5 .U , 4 , 1 0 , 1 9 , L o n d o nM a t h . S o c .3 ( 1 9 7 1 .1) ,8 1 - 1 8 4M

z0l 688. Keogh, F. R. On spiral-likeunivalentfunctions.Notices,A. M. S., vol. 19, no. 2, issue 136, February, 1972(Abstract 692-824), p. A - 3 6 2 .1 6 , 9 , 2 5 , 3 6 1 689. Keogh, F. R. On spiral-likeunivalentfunctions. NoticesA. M. S. 20(Jan. 1973),Abstract701-30-7 , pg.A-105 . 16,7l 690. Keogh, F. R. A characterisationof convex domains in the plane. NoticesAmer. Math. Soc., January 1975,Abstract 720-30-1,p. A- I 18. [201 691. Keogh, F. R. A charseterizationof convex domains in the plane. NoticesAmer. Math. Soc. 23, January 1976,At-,stra:t7'Jl-30-22, p. ,{-103. [20] 692. Keogh,F. R.; Ba;goze,T. The Hardv classof a spiral-iikefunciion and its derivative. Proc. Amer. Math. Soc. 26(1970), no. 4, 266-269. [5, 6h MR 4l #8680 693. Keogh, F. R.; Merkes, E. P. A coefficient inequality for certain of anolyticfunctions. Proc. Amer. Math. Soc. 20, January, classes 1 9 6 9 p, p . 8 - 1 2 :M R 3 8 # 1 2 4 9 [. 5 , 6 , 1 0 , 2 2 , 3 0 ,3 6 , 3 8 , 5 4 , 7 5 ] 694. Keogh, F. R.; Miller, S. S. On the coefficients of BazilevidfuncMR M #424.11, t:ons.Proc. Amer. Amth. Soc.30(1971),492-496; 4 , 5 , 4 9 , 7 0 ,8 l l 695. Kirrrchi, K. Starlike and convex mappings in s€v*€ralcomplex varit,bles.Pacific J. Math. 44(1973),569-580.[l, 6, l0] 696. Kim, W. J. The Schwarzianderivativeand multivalence.Pacific J. MR 40 #5849.[4, 3l] Math. 3l(1969),717-724; P. On an integral of powers of s spirallike Y. Merkes, E. Kirn, 697. J.; J'unction Kyungpook Niath. J., vol. 12, no. 2, December1972,pp. 249-253;MR 47 #8834. [4, 6, 85] 698. Kim, Y. J.; MeikcS, E. P. On certain convex setsin the spaceof locallyschlichtfunctions. Trans. Amer. Math. Soc 196(1974),217224;tdR 50 #2474.[5, 10, 851

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e0l of uni;'alentJunc(Kiriackis,E:1 ccridin ciQsses 700.Kir,jackii, E. c. Germansummaries)Litovsk' lv{at' tions.(Russian.Liuhuarrianand Sb.12\1g72),no'3,75-84'207;IVIR47#5243't281 cert;oinclassof rational univelentfunctions' 1cl. Kir,jackii, E. G. A Litovsk' Mat' sb' (Russian.Lithuanian and German summaries) 1 3 ( 1 9 7 3 ) , t r o ' 2 , 7 g - 8 9 ' 2 5 9 ; M R 4 8 # 2 3 6 3 ' t 2 8 irear funcriuns' pr:obtemsfor the typicaii-t 102. Kirwan, v/. E . Extremar i3, 431 #2853,U2' MR 34 Amer. J. Math. 8g(196,6;,942-954; T03.Kirwan,w.E.Anoteonextremalproblemsforcertainciassesof anolyticfur,ctions.Proc.Amer.Math'Soc'17(1966)'1028-1030; , , 10,241 M R 3 4 # 2 8 5 4 . 1 2 , 56 domains' for a classof bounded Koebe'constant 704. Kirwan, w. E. The A n n . U n i v . M a r i a e c u r i e - S k t o d o w s k a S e c t ' a ' v7ll ol'21(1967)'Nos' 10' l6' 22' l-8, pp. 5-9( 1972);MR 48 #4294'[l ' typically realjunctiotts. ?05. Klrwan, w. E. on the rate of growth of DukeMathJ.35(1968),9_20t;MR36#2805.[13,62] T o 6 . K i r w a n , w . E . o n t h e c o e f f i c i e n t s o f f u ngos) c t i o n277 s w-282' i t h b oMR u n d e38 d , J. istt boundary rotation Mich. Math. # 1 2 5 0 .1 3 ,7 l , 7 7 1 T0T.Kirwan,w.E.Extrematproblemsforfunctionswithbounded boundaryrotation.Ann.Acad.Sci.Fenn.Ser.AIMat.No.595 ( 1 9 7 5 )i,q P P' 1 4 , 2 ! , 2 4 ' 4 3 ' 7 1 ' 7 6 1 and proble^' io' functions meromorphic 708. Kirwan, W. E. Extremal January Amer. Math' Soc' 23' univalentin the unit disi. Notices 25' 58] lgl6,Abstract 731-30-19'p' A-102' [9' extremepoints and supportpoints ?09. Kirwan, w. E.; Schobef,G . on ' J' 42(1975)' uni'valentfunctio"' Duke Math for sornefamilies of 285-296;MR 5l #3416'[6' 9' 88] maioration de K' Yosida' Nagoya Tl0. Kishi, M. Sur le prfnrf), de 33-36' tll; MR 4r #3796 Math. J. 3?(1970), diameterwith applications ?r. Klein, M. Estimatesfor th-e'transfinite toconformolmopping.PacificJ.Math22(|961),267_2i9;MR37

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26r-265.1

the solution of extremal 718. Kocur, M. F. on q new Q-methodfor that are problems in certain specisl classesof analytic functions positive;'ealpart in the disk' (Rusconnectedwithfunctions having-prikl' Mat' (Kiev) vyp ' l7(1972)' sian. English summary)vycisl'

t2l r52-t62;MR 46#s628'

de fonctions certaines sous-closses 7\g. Koczan, L.; Szapiel,W. Sur (Russiansummary)' Bull' Acad' Polon' Sci' Qpique'mrnt MR 49 #5356' Astronom.Phys.22(1974),115-120; ""it"' 56r. Sci. Math.

t13l von Potenzreihen720. Kohlhammer, Hans-peter. schtichtheitsradien abschnittenschlichterFunktionen.GesellschaftfurMathematik u n d D a t e n v e r a r b e i t u n g , B o n n . B e r . N o . g g , G e spp' e l l s c h a431 ftfur 120' Bonn, 1975'90 Datenverarbeitung. und Mathematik preciseorder of the bestapproximations izl , Kokilasvili, v. M. on the generslizedgop series with of analytic functions ,rpirrrrtable by r e s p e c t t o F a b e r p o l y n o m i a l s . ( R u s s i a n . G e o r g i a n sMR u m m34 ary). 4l(1 966), 529_534; Scobsc. Akad. Nauk Gruzin. SSR #78r1.t53l

derivativeof o merornorphic 722. Kolokol'nikov,A' S. The logarithmic {7529' Zarnetkil5 (1974),71t-718;NiR 50 function (Russian)tutu,. tel analyticfunctions wirh positive 723. Komatu,Y. On meonCistortionfor J. 23(1966),?Zl-228; MR 34 real Port in a circic' Nagoya l'{atn. #7807. 12, 561 remark on distoriton for fourth 724. Komatu, Y.; Nishimiya, H. A derivativeoffunctionsreguiurandunivalentintheunitcircle.Sci. MR3911427'142'631 Rep.SaitamaUniv'Ser'eO'(1968)'3-4

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104-108; sian)ukrain.Mat.z. lrltgos),no.4,

737.Kovari,T.;Pommerenke,Ch.onFaberpolynomialsandFober nxpanitons'Math' Z' 99(1967)'193-206't53l of Fekete points. ch. on thedistribution 73g. K6vari,T.; pommerenke,

lf-.-,

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Mathematikal5(1968),70-75;MR38#316'[68] Prelimi739. Kronstadt, E. Compact families of univalent .functio'ns' Abstract 1976, nary report. NoticesAmer. Math. Soc. 23, January 7 3 1 - 3 0 - 2 5P, . A - 1 0 3 . univalent analytic i40. Kruskal', S. L. Some extremal problems for 754-757; Nauk sssR 182(1968), functions. (Russian)Dokl. Akad. MR 38 #3429[sovietMath. Dokl. 9(1968),1l9l-1194]' 1,4l. Krzyz, Jan. on the region of variability of the ratio f(z)/"f(zz) sumwithin the clossS of univslentfunctiorzs.(Polish and Russian A. 17(1963)' maries)Ann. univ. Mariae curie-SklodowskaSect. MR 34 #323' 124,29, 681 55-64(1965); regular in on 742. Krzyz, J. on a theoremof Kubo concerningfunctions annulus.colloq. N{ath. l6(1 967), 43-47;MR 35 #1767't241 functions. syrrposia on Theoreii743. Krzyz, J. G . On close-to-convex Madras' cal Physicsand Mathematics,Vol. l0(Inst. Math' Sci" 1969),pp.23-27. Plenum, New York, l9i0 MR 4l #5610't5l Mariae Cr"'rie7M. Krzyz, i. en extremallengthproblem. Ann. Univ' 95-lM' Sklodowska,Sect. A., vols. 22/23/24(1968/1969/1970),

t4el

a 745. Krzyz, Jan G. The Greenfunction of domains containing fixed r0, etlipse.MichiganMath. J. 20(19i3), 1 3 - 1 9 ;M R 4 6 # 9 3 1 4[.1, 6 , 16,19,491 of smoll degree' 746. Krzyz, ran; Rahman, Q. I . univalent polynomials (1967), 79-90 2l Ann. Univ. Mariae curie-Sklodowska Sect. A (,1972); MR 48 #ll47l. tl 6,20,32, 43, 73' 851 classesoJ 747. Krzyz, Jan; Reade, M. O. Koebe domainsfor certain MR 35 analyticfunctions. J. D'analyseMath. l8(1967),185-195; # 3 0 5 0 [. 5 , 6 , 1 9 , 3 9 , 4 1 , 4 t , 4 9 ] with 748. Krzyz, J.; Zlotkiewicz,E. Koebe setsfor univalentfunctions A I No' 487 two preassignedvalues.Ann. Acad. Sci. Fenn' Ser' (197i), t2 pp.; MR 43 #7612.15,6, l0' l9l to aigehatc 749. Kubota, y. On extrematprcblems witich corresporid 412-428; univalent functions. rooai Math. Sem. Rep. 25(1973), MR 49 #563. 19, 24, 25, 29, 53, 541 urtivalent 750. Kubota, Y. On the fourth coefficient of meromorphic 26(1974/75),267-288' 19, 251; functir,ns. Kodai Math. Sem. Rep.

l,4R52 #7321 meromorphic' 751. Kubota, Y. A coefficientinequolity for certain 94; (1974/75),85unbalenifunction,r'.Kodai Math. Sem.ReP.26 MR 5| #5915.[9, 25, 391 with t52. Kudelski, F. A variationalformula for starshaPedfunctions

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reulcoefficients.Bull.Acad.Polon.Sci.Ser.Sci.M ath. MR 30 #3203.[6, 24,39| Astronom.Phys. |2(|964),6|7-6:Igi classof .ij3. Kudelski, F. On the uniualenceof Taytor sums for a Ann'tJniv' R'ussiansummaries) univalentfunctions. (Poiish and A 1?(1963),65-67(1955)'MR 33 Mariae curie-skiodowskaSect. #5864.[20'43]

-.1

'

'

't-1^-:^)^^{nnnrinnt

quelquesprobr\me.sde ro thtorie desfonctions i54. Kucelski,F. sur summaries).Ann' Univ' subordonn4es.(polish and Russian MR sect.A 27(1973L43-48(lgi 5)' [1]; Mariaecurie-skiodowska 52 #84rr of condirions for the univarence sufficient certain N. S. Kudrjasov, 755. t h e ' s o l u t i o r t o f a n e x t e r i o r i n v e r s e b o u nno' d o r 3(46)' y p r o b105-l l e m .l0; (Russian) 1965' izv. vyss. ucebn. zaved.Matematika MR 3r #s970.t4I of ccnditionsfor the univalence 756.Kudrjasov,S. N. certainsufficient the theoryof filtration' (Rusa solutionof the inver* piiUiem in |966,no. 5(54),88-99; sian)Izv. Vyss.Ucebn. Zaved.Matematika I\IR 34 #606:' t4i -., .-^^ ^{ nmnt,,t' the univalence of analytic criteria for certain N. s. 757. Kudrjasov, Notes

Mat. zametkil3(1973)'3:9-366lMath' functions.(Russian) 9l 13(1973) ,2rg-2231;MR 47 #7022'14' cf G'M' Goluzin'(Rusvariational formula The o. P. Kufarev, 758. s i a n ) T r u d y T o r n s k . G o s . U n i v . 1 6 3 ( 1 9a6 3 ) , 5 8of -62.t241 of family univaletft S. v. A pr-operty 759.Kufarev,P. P.; Soboleva, Tomsk. Gos. Lrniv. Ser' Meh'-Mat' functions. (Russian;irudy 175(lglq),Vvp' 2, 5-7;MR 3l #5979'l9l ,160.Kufarev,P.P.;SoboleV,V.V.;Sporysev&,L.v.Acertainmethod problims for functions which are of invesrigationo7 exiremal Trudy Tomsk' Gos' univ' univalentin the noti-p,tinr.(Russian) 571 MR 41 #1987.124, 142-164; 'die ser. Meh._Mat.200(1;68), suf Abbitdung schlichtekonforme 16l . Ktihnau, Reiner. uber 37 MR 6l-7 i; Gebiete.Math. Nachr.36(1968), nichti)berlappende #2969. bei quasikonformen j6z. Kiihnau, Reiner. Koeffizientenbedingungen Ann' univl Mariae Abbildungen(Polishand Russian"'*-uties) i05-l l l(1972);M* 49 Sect.A zz-24(1968/70), cruie-sklodowska # 7 4 4 11. 4 , 3 15, 3 1 isch-funktionentheoretischeLbsung j 63. Kiiirnau, Reiner. Geometr ' J' Reine 4bbitdung eines Extremal problems der knoformtn #7434' MR 40 131-136; Angew.Math' 229(1968)' schlicht gewisser ,7&. Kiihnau,Reiner. Sc-hran'ken 7u, die Koeffizienten

hr-----

194

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

Nachr' 4l (1969)' 177 abbildenderLaurentscherReihen. Math. ' [9' 25] t83; MR 40 #32'7 den Rundungsund Stern765. Ktihnau, Reiner. Diskretisierungenzu Rev' RoumaineMath' Pures schrankenbei konformer Abbitdung' , !229-1234;MR 42 #471e'[121 Appl. 15(1970) Bemerkungenzur Theorie der 766. Kiihnau, Reiner.Weitereelementare Math' Machr' konformen und quasikonformen Abbildungen' ' 5 1 ( 1 9l/) , 3 7 7 - 3 8 2 ;M R 4 7 # 3 6 5 7 Arbeiten';on o' Dvorhk' 76j. Kiihnau, Reiner.Eine Bemerkungzu zwei M a t h . N a c h r . 4 8 ( 1 . 9 7 1 ) , 2 2 5 - Z Z O ; M R 4 5 # 5 3 2 b ' t 4 2 1 Math. schlichter Funktionen. 76g. Kiihnau, Reiner. uber vier Klassen Nachr. 50(1971),17.-26;MR 46 #9315'[53] schlichter konformer Ab769. Kiihnau, Reiner. uber zwei Klassen MR 48 #4300't241 bildungen.Math. Nachr. 4g(lg7l), 173-185; schticht abbildende 770. Kiihnau, R. Koeffizientenbedingungenfi)r summaries)Bull' Acad' LaurentscheReihen. (English and Russian Polon.Sci.Ser.Sci.Math.Astronom.Phys.20(197?),7-10;MR 48 #6397.[48' 53] 77|,Kuhnau,R.ZumKoeffizientenproblembeidenquosikonformfortMath ' Nachr ' setzbaren schlichten konformen Abbitdungen 25' 541 55(l g73),225-231;MR 48 #522' [9' konformer Abnichtschrichter iiz. Kiihnau, Reiner. Eine Krasse bitdungenmiteinerscitlichtenquasikonformenFortsetzung.Math. Nachr. 59(l 974),261-263;MR 49 #7M2' Ableitung bei der Schwarzschen 77i. Kilhnau, Reiner. Zur Abscitiitzung 59(l 974)' 195-198;MR 50 schlichtenl.-unktionen Math. Nachr' 31]

#594. [4' . , - . c ^ ,) ^1'nnDr, symmetrrc j j 4 . Kulshrestha, p. K. Coefficient bounds for k-fold u n i v a l e n t J - u n c t i o n s o f b o u n d e d r o l g t i o i l . N o t ip. ces,A.M.s.,vol.l9, 696-30-7), A-631.[4,9, no.5, issue139,August, 1972(Abstract i !, 1'il Ti5.Kulshrestha,P.K.Distoritonofspirnl-likemappin gs.Proc.Rcy. g73),MR 47 #70|6. [6' 63] 1-5(1 A73, Sect. Irish Acad. s' functions. NoticesA. M' 7i6. Kulshrestha,p. K. BoundecrRobertson 36,63,731 t-szl. [6, 12' 20, August 1g73,Abstra ct7C6-30-5,i. mpapings' jj. . Kulshrestha,p . K. Generalizedconvexity in conformol J.Math.Anal.Appl.43(1g73),44|-449;vrn49#g|821,6,29,69, 83,841 778. Kulshrestha,P.K.Coefficientsforaipho-convexunivalentfuncg74), 341-342;MR 49 #7434' tions. Bull. Amer. Math. Soc. SC(l [69, 84]

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195

T T g . K u l s h r e s t h a , P . K . C o e f f i c i e nAnal. t p r o bs+ir t e mg74),205-211; f o r a - c o n v e xMR u n i v51 alent Rationai tvtectr. er.rr. functionr. #878. 123,59, 70' 841 no. T S 0 . K u l s h r e s t h a , P . K . C o e f f i c i e n t p r Math. o b l e m f3l o r(|9-15/"t6), aclassofM o c a3,n u - , Polon. enn. functions. Bazilevic 2 g 1 ' -2 9 9 . i 6 9 , 7 0 , 84]

, ' - (Japanese' / | ^-^h6ca Fnol i sh surnsutn' English hyperbolas' and circles on , Inao 781. Kuroda, mary)Bull.YamagataUniv.Natur.Sci.5(1960),no.l,l|9_|32; t49l MR 4r #3',730. sumnary). .|82. t(g1tlda,Inao. on discsanri strips.(JapaneseErrglish MR 4l sci. 5(ig6t), no' 2' 241-258; Bull. yannagahuniv.-Norur. #3'73?,. t49]

.^nntntal rttto to tn ViktorsLm$' (Japanese sumq theoremdue On ' inuo Kuroda, 783. mary)Bull.YamagataUniv.Natur.Sci.5(1962),Do.3,525-528; MR 4r #7085a.[39] due to of the family of functions sources several Inao. 784.Kuroda, F r i e d m a n o r L i n i s . ( J a p a n e s e s r L r m#7085h' a r y ; B ut39l ll.YamagataUniv. 1-8; MR 41 nl"t ' 6(1963), Sci. Natur. circulqr qnd on figures bounded by two ?g5. Kuroda, Inao . on air,5 Bull. YamagataUniv' Natur' surnmary) Engish (Japanese. arcs. MR 4l #3'732'l49l Sci. 5(1963),no' 4' 807-821; regular' schlicht of ,n', fami! of functions vieiv a . lnao Kuroda, 7g6. summary)Bull' Yamaaisc.(Japanese snd norntarizedin the u"nit MR 3l #2388'[18' 44] garaUniv. Natur. s.i.-itrqo+l,l2g-137; schlicht rn, fmaily of functions regular' Bull ' 7g7.Kuroda, Inao. A vrewit . (Japanese summary) unit ctisc snd normalized in th; z, l2g-137;MR 4l #3738' yamagataUniv. Narur. Sci.6(1964;,nn.

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ofthef:*it',,"f . A view fi,]ii;Jl?1"" 78e. ,{::::::: :,:,Y::,::ol'o' a n d n o r m a l i z e d i n t h e u n i t d i s c .tto. T | .+,383-393; ( J a p a n e sMR e s u4lm#3'139' mary)Bull. yamagata Univ.Nut.rr.sci.etrqoil,

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h---

-

196

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FUNCTIONS

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(LoMIi

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E" b--

2OO

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( P o l i s n a n d R u s s i a n s u m m a r i e s ) A n n . U n i v . M a r i a e C53' urieMR 50 #10236'122' Sect.A 26(tgiz), 17-2g(197g; Sklodowska 611 of sonteclasses A. E,.Cn the univalence E55.Libera,R. J.; Lr.lingst'on, ofregularfunctions.Proc.Amer.Math.soc.30(i9,71),327_336; M R 4 4 # 5 4 4 2[ -5 , 6 , 1 0 ,l l , z , 7 3 ' 8 2 ] functionswithpositive g56. Libera,R. J.; Livingston,A. E. Bounded 45 Math. .I. zz(g1)(lgiz) 195-209;MR reut part. Czechoslovak #'t039. 12, ?'Zl

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bi----

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FUNCTIONS OF SCHLICHT

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(PART TI)

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46 #3',163' [6' Portugal.Ir4ath.30(1971),73-82;MR starlikeness. ll, 12,43,7ll greaterthan cr' Proc' g83. McCarty,carl P. Functionswith realpart g72),211-2i6; l"in 45 #ic66'12'19',21"22', Amer.Math.Soc.35(1 5 6 ,6 1, 7 2 1 cv'Notices with realpart grealer -t-han 884. McCarty,Carl P. Functions rgt-845. 12,,6,12,721 A. M. S., vol. 20(Feb.1913),Abstru.l Notices gg5. McCarty, carl P. some ,lorru of analyticfunctions' ,,42, p. A_487. Abstract74T_B Amer.Math.Scc. 2| ,August|974, 12,12,21,561 with initiatlero coeJficients' '21 gg6. rviccarty,carl p. Anaryticfunctions ' lg74' Abstract74T--869 NoticesAmer. Math io. . , F etruary P. A-309. 12,391 problems'Proc' Amer' gg7. Mccarty, C. p. Tworadiusof convexity 6' 12'21',16',56', MR 48 #4295.12' Math.soc. 42(tg74),153-160t

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, . c ^ - .- ^ t ^ ^ - of n { symmetrrc ctt,r,ytp . Extremalproblemsfor a class 895. Mclaughlin, Renate 4' pp' Mech. Analy., 24(1972),no' Rational Arch. functiotrs. 48' 3 1 0 - 3 1 9[ 1 . 0 ,2 2 , 2 4 , 3 5 ' 6 l ] of oddfunctions g96. Mclaughrin,R.,4 ;aria*ionarmethodfor a cras,s 451 973),299-305'12+' in an annurus.colloq. Math. 28(l problemsof analyticunivalentfunctions 897. Mcleavey,J. O. Ex:tiemal

\.-_

204

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w i t h q u a s i ' c o n f o r m a l e x t e n s i o n s . T r31' a n s531 .Amer.Math.Soc. 124' #10880' 49 MR Acta 195(l974),327-343; ii o conformal mapping' g9g. McMillatr, J. E. Boundary behaviof

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;:'

u,)', or quotient iifrerence minimum MR

rnruitr.so. . qiog6i), z''l-26g; univarent functions.J. Lrndo, 35 #360.ito, t 2, 16'64' 681 9 0 6 . M a c G r e B o f , T . H . , C e r t a i n48'-;iI{R I n t e g r a l 36 s o#5324' J - Y ! i '[1', y : '4', ; , ,5', t a6', n 10', dConvex Functions.Math.2. twtl968), 16, 47 ' 64' 851 a -^ :-nn,,nrit concerntng onalytic functions gO7. tutu.C"go'' i' H' An inequality ll'72-ll7'7; Math'' 21(1969)'

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205

J. 19(1912),tro' 4, pp' univalent functions. Michigan Marir. 3 6 1 - 3 7 6 ; M R 4 7 l ' 4 4 7 ' [ l ' Z ' l ' 5 ' 6 : 1 0 ' 5 6 ' 6 3 ' 6 4 ' 7 4 ' 7 5problems '88] and extremul gr 3. rviacGregor,Tiromas H'. Hutt subordination 183 n:appirtgs.Trans' Amer' Math' Soc' for slartike'aridspiratlike 20' 881 (1973),499-510;MR 49 #3104'tl' 6' 10' the Rcnge of an analytic gl4. MacGreBcr, rhomas H. Rotationsof '14'16'24' g 7 3 ) , I I 3 - i Z O t; U n 4 8 # 6 3 9 0 f u n c t i o n f v i u t t .A n n . 2 0 1 ( 1 49,54,681 of ordera' gi5 ivlacGregor,T. H. -4 subcrdinationfor convexfunctions IviR 51#31|7.u,6, lOj g(rg75),530_535; J. London Math. Soc.(z), pri;t rt differentiablefunctionals and support 916. MacGregot, T. H. NoticesAmer' Math' Soc' pointsfor famities cf analyticiunctions' p' A-100' [6' 881 23, JanuaryI 976,Abstralt 7i1-30-11' ' (Polish and Russian gli . Mak6wk&, B. Quasiy-spiratstarlikefunittont L6d2' No' 208 Mat' No' srrmmaries) Zeszyty tiaut Politech 6 (1 9 7 5 ), 4 7 -7 5 ' t6 l ; I\' IR 52 #72i

,, ^,---^nl nti oti ,. ttr nnntvl i a geometricalcharacteristicof anolytic 918. Malec, M.; Nikitch, N. on functions.(Polishsummary)ZeszytyNauk.Akad.Gorn.-Hutniczej. t35l MR 50#10212'

. zesrytriirqzlj, 133-t35; Mat.-Fiz.-chem (Abstract),Notices, of a porynomiqr. on therlerivat-ive

9t9. Malik. M. A. 'ran' lgSg'p' 290' 127'321 A. M. S., vol. 16,no' f issueno' 111' transformation'capacityand con920.Marcus,M. A radial averaging f o r m a t r g d i u s . B u l l . R m e r . M u t H . s o . . T s arcs ( I 9 7of 2 )rever , 4 5 6curves -460.|241 gzr. Martynov,Ju. A. Thegeometricpropertiesof Trudy Tomsk' Gos' (Russian) underschlichtconformot^oppings. 53-6i;MR 43#5016.12,12'29',351 Univ.Ser.Meh.-Mat.210(1q69), functions' g22. Mathews,J. H. Coeficientsof yltf:rmly normol-Btoch Y o k o h a m a M a t h . J . 2' l ( 1 g 7 3 ) , 2 9 - 3 1 ; M R 4 8 3 2 1class ' of in# 4the g2t . Matsrur^oto,K. Note on Schiffer's voriation NagoyaMath' J' 32(1968)' univalentfunctionsin the unit disc. 273-276;MR 38 #1247' 124'421 for certqinfamily of func' gz4. Mazur, R. on the radiusof B-convexity Math. 8(1975\, Demonstratio tionsmeromorphicin the-u.nitdisc. . 12,l2l; MR 52 #8404 483-489 , of a certatnrng25.Mehrok,T. J. S.; Bajpai,s. K. o.n the univalence [6, 10,851; 5(1g74),186-191' N,lath. l. puJ, a',ppt. tegrat.indian MR 52 #350r growth of typicallyreaifunc926.Merkes,E. P . on convolutionsand to A' J' Macintyre'pp' 299DedicateJ Essays tions.Mathematical 1970;MR 42 #?880'[12' 13' 303.ohio Univ. pr.*, Aihens,ohio, 41,47, 621

b.-*

206

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g27. Merkes,E. P.; Scott,W. T. Coveringtheoremsfor univalentfunc' 6, 10, tions.MichiganMath. J. l3(1966),4I-47; MR 32 #7729'[1, 19,22,301 g28. Merkes, E. p.; wright, D. J. on the univslenceof a certqin int e g r a l .P r o c .A . M . S . 2 7 ( l 9 7 1 ) , 9 7 - 1 0 0M; R 4 2 # 4 7 2 0 . 1 2 , 4 , 5 , 6 ,

10,851 E. P.; Wright, D. J. Typicatty.reqlpolynomiols of smafi 929.Merkes,

degree.Math. Student39(197l), 205-206(1972);MR 48 #8762.ll3 ' 3?j 930. Miazga, J. The radius of convexityfor a classof regularfunctions' (Polish and R.ussiansummareis) Ann. univ. Mariae curie-35(l 970; MR 50 #10226' 16, l2l SklodowskaSect.A 26(1972),3 I of convexi931. Miazga, J.; Stankiewicz,Jan; Stankiewicz,Zofia'Radii univ' ty for some classesof close-to-convexfunctions. Ann. 46 MR 53-57(1971); Mariae Curie-sklodowskaSect.A 20(1966), #3765. [5, I 2, 701 g32. Michel, c. Eine Bemerkungzu schlichtenFolynomen. (LooseRusser. Sci' sian and English summaries)Bull. Acad. Polon. Sci. 9 ;R . 4 3 # 6 4 2 3 [. 3 2 ] M a t h . A s t r o n o m .P h y s .1 8 ( 1 9 7 0 ) , 5 1 3 - 5 1M g33. Mikka, V. P . Sufficient conditionsfor the univalenceof the solupoints ' (Rustionsof inverseboundary valueproble,ztswith corner MR 50 sian) Trudy sem Kraev. zadacamvyp. 10(1973),95-106; #6?,0.l4l g34. Mikolaj czyk,L. certain properties of extremal univalentfunctions thatarep-Symmetricandboundedfrombelowinthedisc1z|> (Polish. English summary) zeszytyNauk. Univ . L6d2k Nauki Mat' Przyrod. zeszyt20 Matematyka(1966),103-115;MR 50 #13483' 19, 24. 49, 581 pour lesfonctions 935. Mikolaj czyk, L. Theoremesur ta deformation univalentis p-symetr!queset borneesinferieurment dans le domaine

lzl

581 Astrono*. ptrur. l4(l 966),245-250;MR 34 #330.19,24,49, et 42 936. Mikolaj czyk, L. Le domaine de variablilite des coefficrents reels' 43 ctesfinctions univalentes bornees avec des coelficients Math' Sci' 56r. (Russian summary) Bull. Acad. Polon. Sci. MR 34 #331.122,291 Astroncm.Phvs. 14(1966),251-254; g37. Nlikolaj czyk, L. Domqine de vsriation des coefficients '42 et As Polon' desfonctions univalentesborneesa coefficientsreels.Ann. Math.lg(1967),81-106;MR35#352'i22,29'391 univalent 938. Mikolaj czyk, L. A theorem on distortion Ju' circte the lzl p-symmetiicatfunctions bounded in

BIBLIOGRAPHY Oi SCHLICHT FUNCTIONS

(PART ID

201

35-51;MR 38 #2294'19' 22' 241 12(1968), a schlicht g3g.Mikolaj czyk,Leon. Relation betweenthe modulusof f u n c t i o n , p - S y m m e t r i c a l a n d b o u n d e d f rary) o m bzeszrty e l o w ,Nauk andthe moduhtsof itsderiveiive.(Polish.Frenchsumm 29(1968)'3-29; Univ. L6d2k Nauki Mat. Przyrod.56r' ll zeszyt MR 39 #7082.[9, 49, 58] of a schlicht g40.Mikolaj czyk,Leon.,nritation betweenthe modulus and the modurusoJ'itsderivative. function rita'tis bouncedberow Mat' summary)zeszytyNaukUniv 'L6d2k"Nauki (PcHsh.Errglisi), 3-2t;MR 4| #450.[9' 581 Przyrod.5617|7'eszytl-+,1i969), (e) - pf (g) g4l. Mikolaj czyk,Leon.A cer:tainsolutitrnof theequationf (Polish'Englishsummary) in the classof a-spiralsturli!:cJuncrrs' Przyrod.Ser.Il zeszyt zeszytyNaui
H--

20E

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

Report 7225; Naval Research cients of Schlicht functions' NRL f ii + 164pp.; MR 43 #5017' Laboraiory, Washington,D' C '' l97

t53l

9 5 0 . M i l l e r ,J . E . Convexmeromorphicmappingsandrelatedfunctions. MR 4l #3740'12' 5'9' ZZO-ZZI; Proc. Amer. Math. Soc.Z5t(llrO;, 1 2 ,5 6 , 5 8 1 meromorPhic univalent 9 5 1. Miller, James. Extremal functions for -86; 44#s443 . , 24,

f

y ii,Lr:l :i"aryseMath. zAe D:77

MR

te

58,681 Proc' Amer' g52. Miller, James E. stcrrlikemeromorphicfunctions' M a t h . S o c . 3 l ( 1 g 7 2 ) , 4 4 6 - 4 5 2 ; M R 4 4 # 5 4 6 5 ' [ 6 ' 7 ' 9Pacific ' 5 8 1 J' functions' quasi-subordmate of sequences E. 953. Miller, J. M a t h . 4 3 ( 1 g 7 2 ) , 4 3 7 - # ;M2R 4 7 # 7 0 2 3 ' t l l modul,ls for meromorphic 954. Miller, James. on the maximum Virginia Acad' Sci' 45(1973)' univalent functions. Proc. west 360-365;IvIR 50 #10237' 19' Z4l ? for convex mops tn g55. Miller, J. E. subordinotingfactor sequences 1g74,AbstractTlT-Bl7' C'. NoticesA. M. S., vol. 21, Nov.-t.t P . 4 - 6 1 4 . t l , 1 0 ,4 7 1 of a Bqzilevii funciion cnd its 956. Miller, s. s. The Hardy class Soc. 30(197:r'1,|25_|32 \IR 44 derivqtive. Proc. Amer. Math. # 5 4 M . 1 3 , 4 ,1 6 , 6 2 , 7 0 ,8 l l f , n-fold symmetrrc g57. Miller, Sanford S. An ari-tength problen' for univglentfunctions.KodaiMath.Sem.Rep.24(|972),|95_202:'

M R 4 5# g b n .t 5, 6 , 7 , 1 0 ,3 5 ,4 9 1

functions' of alpha-starlike 95g. Miller, S. S. Distortion'properties 19' proc. Amer.Math. Soc.:'atrg:3),?tt-318;MR 46 #9324'14, 6 2 , 6 9 ,8 3 1 funciions.II' for crphc-convex g5g. Miller, Sanfords. TheHp crasses p' 1g74,AbstractT4T-880' NoticesAmer.Math. soc.2l, Aprit A-371.[6e] of bcurtdedargument of 960. Miller, s. s. TheHardy class functlcns February1974'Abstract rotation NoticesAmei. Math. Soc' 21, 74T-834,P. A-30i ' [62'71] functions. and carath€odory 961. Miller, s. s . Differeirtoiiniquarities # 7 5 3 31' 2 , 6 9 1 5 0 M R B u l l .A m e r .M a t h .S o c .8 1 ( i 9 7 5, 7) g - t _ 1 ; The boundedness' implying 952.I'{iiler,S. S. A d'Jfeientialinequatity (Ad1975 Monthly, vol . 82,no. 5, May AmericanMathematical vancedProblemsDepartment),p.529.|221 differential inequalitics implying 963.Miller, s. s. A iirt of y 1975'Abstract Noti.es^t.r. Math' soc.' Januat boundedness. 720-30-16, P' A- 122'l22l

I

BIBLIOGRAPHY OF SCTILICHT I]UNCTIONS(PAR,TII)

964. Miller, S. S. Second order differential inequalitiesand sorne applications in univalentfunction theory. NoticesAmer. Math. Soc. p. A-100. [2] 23, January1976,Abstract731'-30-10, -l'. T-heHgrdy c/al-'c'ffunctlons 965. Miller, Sanford S.; Mocanu, Petru Math. Soc. Ser. A 2l Austral. J. roiation. of boundedargument (1976), no. I , 72-i 8. t71l 966. Miller, S. S.; Mocanu, P. T.; ReaCc,M. O. Ali d.-convexfunctions ore starlike. Rev. Roumair.e Math. Pures Appl. 17(1972), MR 48 #2364.[4, 6, 9, 12, 69, 841 1395-1397: g57. Miller, S. S.; Mocanu, P. T.; Reade,Malwell O. The ru,lius oi ( a-convexity of rmivalent fltnctions, I < 6v @. @reliminary report) NoticesA. M. S. 20(Feb.1974),Abstract73T-860. U 2. 691 are 968. Miller, S. S.; Mocanu,P.; Reade,M. O. AII a-convexfunctions (1973), 553-554; 37 Soc. univslentand starlike. Proc. Amer. Math. MR 47 #2044.[6, 10, 691 969. Miller, S. S.; Mocanu, P.; Reade,M. O. Bazilevii functions and generalizedconvexily. Rev. RoumaineMath. PuresAppl. l9(1974\' 213-224;t{R 49 #3105.[4, 12, 16,68, 69,701 970. Miller, S. S.; Mocanu, Petru T.; Reade,M. O. The HarCy classes for functionsin the classMVla, kl. J. Math. Anal. Appl. 5l(1975)' 33-42.[71]; MR s2 #728 g7l. Minsker,Steven. ,4 newproof of Pick'stheorem.J. Res.Naf- Bur. StandardsSect.B 78B(1974),95-96;MR 49 #10873.14,22,301 972. Miro5nidenko, Ja. S. Certain extremalproblems of the theory o"f univalent functions. (Russian) lzv. \'yss. Ucebn. Zaved' Matematike1965,no .2(45).104-109;MR 32 #2574.[Amer' Math' . 17, 9, 35' 451 Soc. Transl. (2) vol 88(1970)l g73. Mirolnidenko, Ja. s. On the question of the curvature of level curves. (Russian)Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat. 210 (1969),62-65;MR 44 #6950.[35] gj4. Mitjuk, I. P. (Jnivalentconformal mappingsof multiply connected domain (Russian)Problemsof Math. Phys. and Theory of Functions, II (Russian),pp. 74-84. Naukova Dumka, Kie", 1964;MR 32 #5856.17, 18, 491 975. Mitjuk, I. P. Some properties of functions regular in a multiply connectedregion. Dokl. Akad. Nauk sssR 164(1965),a95-498; 124,601 MR 32 #5862.{soviet Math. Dokl. 6(1965),1252-1255]|. gj6. Mitjuk, I. P. The symmetrizationprinciple for an annulusand certian of its applications. (Russian) Sibirsk. Mat. Z' 6(1965)' 1282-1291;MR 35 #4396.[14, 24,33, 48] 97j. Mitjuk, I. P. The inner radius of a domain and certainof its proUkrain. Mat. Z. l7(1965),no. 1,ll7-122;MR32 perties.(Russian)

+

_

__

2IO

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

# 7 7 3 0 [. 1 4 , l 9 ] in an annulus' 978. Mitjuk, I. P. Some theoremson functions regular (ukrainian. Russian and English summaries) Dopovidi Akad. ; R 3 0 # 4 9 2 6 . [ 1 41, 9 , 3 3 , 4 8 ] N a u k u k r a i n . R s R 1 9 6 5 ,1 6 0 - 1 6 3M gig. Mitjuk, I. P. The principte of symmetrizationfor multiply conat' nectedregionssnd certain of itsapptications.(Russian)Ukrain' Z. t7(1965),no. 4, 46-54;MR 33 #7510'[6' 18] regular in 980. Mitjuk, I. P. Some covering theoremsfor functions muttiptl;-connecteddomsins. (ukrainian. Russian and English summaries)Dopovidi Akad. Nauk ukrain. RSR 1965, 550-554;

MR 33#28r1. u9l

regular func981. Mitjuk, I. P . A certsin subordination principle for 189 tions. (Russian)Trudy Tomsk. Gos. univ. Ser. Meh.-Mat' ( 1 9 t t 6 )1, 6 1 - 1 6 7M ; R ] 7 # 4 2 4 4 '[ 1 , 7 , 1 8 ] g82. Mocanu, P. T. Extremal domains in the clossof univalentfuncR' P' tions. (Romanian. Russian and French summaries)Acad. 30 MR 303-313; Romine Fil. Cluj Stud. Cerc- Mat. 12(1961), #4939.124,291 gg3. Mocanu, p. T. On an extremqlproblem relativeto univalentfuncR' P' tions. (Romanian. Russian aird French summaries)Acad. #5868' Ronine Fil Bluj Stud. Cerc.Mat. l4(1963),85-91;MR 33

l24l

9 8 - 4N . { o c a n u , P . T . O n the radius of convexity of holorr'orphicfuncUniv. tions. (Romanian. Russian and French summaries)studia MR 30 Babes-BolYaiSer. Math.-Phys. 9(1964),no. 2, 31-33; # 4 9 1 8U . 2,3ll - af(u) in the class of 985. Mocanu, P. T. On the equation f@ MR 32 univalentfunctions. Mathematica(Cluj)6(29)(1964)63-7e;

#773r.I24l

(Romanian)Stud' 986. Mocanu, P. T. Functions univalent an sectors. Cerc.NIat.i?(1955),925-931;MR34,M7514'57'l gg7. ivlocanu, p. T. Generulizedradii of stariikenessand convexity of Studia analytic functions. (Romanian and Russian summaries) MR 43-50; 2, no. (1966), l1 Ser. Math.-Phys. univ. ga-bes-Bolyai 3 5 # 6 8 1 0[.1 1 , 1 2 , 3 1 1 map988. Mocanu, Petru T. Convexity and starlikenessof conformol #5600' [6' pings. Mathematica (cluj)8(3 lx I 966), 9l-102; MR 35 10,I l, l2l of the exponen989. Mocanu,Petru T. About the radius of starlikeness Univ' tiat function. (Romanian and Russian summaries)Studia 41 MR 35-40; -Phys. 1, no. 14(1969), Babes-BolYaiSer. Math ' #1990.[6, I l, 23]

(PART TI) BIBLIOGRAPFIYOF SCHLICHT FUNCTIONS

2II

dans la gg0. Niocanu, Petru T. (Jnepropritt| de convexit, g€n'ralis€e (cluj)ll(34) th€orie de ta repr€sentationconforme. Mathematica (1969),127-133;MR 42 #7881'[6' l0' 12' 691 de ra reprlsentation conforme. 991. Mocanu, petru T. sur ra g,6on6trie 299-308;MR 48 #6391't6' l0' 351 Mathematica(Cluj)12(35)i1970), ggz. Mocanu, P. T. An ,*tir*ol problem .for univalent functions curiewith the Darboux formula. Ann. univ' Mariae associated 1970),p' 13l-135; Sklodowska,Sect.A, vols. 22,/23/21(lg6s/1969/ MR 49 #5335.[4' 16i dans la gg3. Mocanu, petru T . sur deux noiions ce convexiti g1niralis1e Russian summaries) repr€sen.totionconforme. (Romanran and 16(1971),tasc' 2' Studia univ. Babes-BolyaiSer. Math.-Mech. 13-19;MR 47 #366s'tl0l in conforgg4. Mocanu, petru T. A generatizedproperty of convexity malmappings.Rev.RoumainesMath.PuresAppl.l?(1972),13911 3 9 4M ; R 49 #5327'U2,35,491 , , th60rie , , < ^ - : ^de ) gg5. Mocanu, petru T. Sur unepropircte d'etoilementdans la R'Omaniansummaries) la representationconforme. (Russian and 17(1972)'fasc' 2' Studia univ. Babes-BolyaiSer. Math'-Mech' 5 5 - 5 8 ;M R s 0 # 5 8 6 '[ 6 ] the classof starlike 996. Mocanu, pe*,ruT. The radiusof a-convexityfor M' S' 20(Jan' 1973)' univalent functions, a reol. Notices A' Abstract(Prelim.report)701-30-34'p&A-112'U2'691 g97.Mocanu,P..f.; Moldovan,Gr.; Reade,M. o. Numericalcomputa(Romanianand Russiansumtion of the convexKoebefunction. Math.-Mech. 19(1974), maries) Studia Univ. BaLes-BolyaiSer. f a s c ' | , 3 ' 7 - 4 6 ;M R 4 9 # 3 1 C 6t' 6 ' l 0 ' 4 9 ' 6 9 ' 7 0 l of certainuniof starlikenes;s 998. Mocanu, P.; Reade,M. O. The order ' Soc' 18(1971)' 815' vqlent functions. Notices Amer. Math Abstract #7lT-B182. [69] conforg g g . M o c a n u P e t r u . ; R e a d e , M ' O ' O n g e n e r a l i z e ducexity o n in Appl. 16(1971),i 54|_ mal mappings.Rev. RoumaineMath. Pures 1544;MR 46 #7 495' 14' 5, 6 ' 10' 691 d'-convexfunctions' I' 1000. Mocanu, P.; Reade, ft'f. O . Muttivalent Notices,A.M.S.,vol.19,no.6,issuel40,october,|972 p' A-702' ll4' 691 (Abstract'72T-P;280), Notices'A' 1001. Mocanu, P.; Reade,rur o. on a-convexfunctions' M.S.,vol.19,no.2,issue136,February,|972(Abstract693_ B 1 3 ) ,P . A - 3 9 4 ' t 6 9 l rodius of a-convexity 1002. Mocanu, petru T.; Reade,Maxwell O. The ofcertainclassesofstartikeunivalentfunctions'areol'Proc' Amer.Math.Soc.5l(1975),395-400;Rev.RoumaineMath.

>|--

-

2|2BIBLIOGRAPHYoFSCHLICHTFUNCTIONS

PuresAppl.20(1975),tro'5'561-565;MR51#10604'[6'9'12' 29, 691;MR 52 #3502 E' on criteriafor the 1003.Mocanu,P.i Reade,M. o.; Zlotkiewicz, vol. 18,no. 4, of analytic functions.Notices,A.M.S., univalence p' 637'[69' 70] isueno. 130,June1971(Abstract71T-8104), E' on Bazilevitfunc1004.Mocanu,P.; Reade,P. T.; Zlotkiewicz, tions.Proc.Amer.Math.Soc.3g(1973),|73-174;MR47/2M5. [4, 5, 70] ' On Eligiusz PetruT.; Reade,MaxwellO'; Zlotkiewicz' Mocanu, 1005. thefunctionalV@)/.f,Qz\|,fortypically-reoifunctions.Rev. 3(1974),oo' 2' 209'214 Anal. Numer. Theori. eppi"ximatiorr (1975).U3, 661;MR s2 #s972 E' Bazilevid functions 1006.Mocanu,P.; Reade,vt. o.; Zlotkiewicz, vol' 19' S" M' A' p-valentfunctions'Notices' andclose-to-convex p. A-636. [5' 696-30-l), no. 5, issue139,August,tgiz (Abstract 1 4 ,7 0 , 8 0 ,3 1 1 vonM. Schiffer.Mitt' Math' 1007.Mogk, 8,. Uberein Variationslemma ii + 42 pp.; MR 40 #329'1241 Heft g2(1969), sem.Giessen p'oOti* of a certain clqssof 1008.Mogk, Eberhard.A; external Math' Sern' Giessen schiichtfunctions in an annulus.MITT' ' t48l g2(rg7r),pp. 5 r-54 MR 45 #5357 startike functicns in the unir disc' 1009.Mogra, M. L. on a classof nr. |63, August|975 Notices,A. M. S., vo|. 22, no. 5, iss,re p' A-51l ' [6' 12' 36' 631 (Abstract75T-B158), of univalent certain classes 1010.Mogra, M. L. Radii'o7,"n',exiti for Abstract 1975' Math. Soc', october functions. NoticesAmer. 75T-B190,P. A-625' 12' l2l of Junctionsunivalentin the disc r0r r. Mozgovaja,L. I. on a cra-ss

lzl

I a s i ( N . S . ) 1 0 ( l 4 X l g o + ) , n o . 3 - 4 , 3 7 _ 4 2 ; M R 3 2 # 2 0 5P^ .|4,23| probtems in lhe closses and extrentst certai'n . Aiicja 1012. Moleda, < l ' (Polish' English ShofJunctionshotoiorphic in the disclzl Mat' Przyrod' Ser' Il summary) zeszytyNauk univ . LodzNauki #3117.[6,23,24| Zeszyt52Mat. (1973),57-83;MR 49 deilefunzione univslenti 1013. Montaldo, oscar. sui comportamento summary) Boll' mell,intorno della funzioni ai Koebe. fEnglish U n . M a t . i , ' a - ! . ( 3 ) 2 i ( 1 9 6 6 ) , | 2 7 - 1 4 3 ; M R 3 4 # 3 3 3 . | 2 4 , 5with 4| univalent of functions generalization i lr. J., 1014. Moulis, E. Amer. Math. Soc' 174(1972)' bounded boundary roiation Trans. 3 4 5 - 3 6 8 ; M R 4 7 # 8 8 3 5 ' 1 4 ' 5 ' 1 1 ' 1 2 ' 2 3 ' 3 1 ' t l ' i 6 ' 7 1 theory 1 of cn an ineqr,s1ltyin the 1015. Mozgovaja, L. L; Aciicv, H.

(FA R T l l ) B IBL IOGR A P H YOF S C H LIC H T FU N C TION S

2" t3

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[3]

^.c-.^t.,^- n{

httn fttltf-

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-------

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1161. Pommerenke,Ch. On a varlational ntethod.for univalentfunctions.MichiganMath. J. l7(1970),l-'3; MR 4l #452-l24l 1162. Pommerenke, ch. Normal functions . Proc. hlRL conf . on ClassicalFunction Theory (Math. Res. Center,Naval Res' Lab', Washington,D. C., 1970),pp.77-93. Math. Res.Center,Naval Res.La!., Washington,D. C., 1970;MR 48 #4322.U9,441 1163. Pommerenke,Ch. Esliamtesfor normal meromorphicfunctions' Ann. Acad. Sci. Fenn. Ser. A I No. 476(1970),10 pp'; MR 44 #2928.122,43, 46, 61, 681 (2) 1164. Pommerenke,ch. on Btoch Functio,ns.J. London Math. soc. 2(lg7}),689-695;MR 44 #1799'[16, l9' 621 1165. Pommerenke,ch. on the growth of the coefficientsof analytic

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l4TL Turzynski, A. Problems related to the clossV' of holomorphic (Polish and Russiansummaries) functions of restrictedrotation. zeszytyNauk Politech. Lodz. No. 186Mat. No. 5(1974),61-80; M R 5 0 # 1 3 4 8 5U. 2 , 3 5 , 7 l , 7 7 1 clas-"es 1472. Turzynski, A. On someproblems in the classp* and some generatedby this class.(Polish and Russiansurnmaries)zeszyty 50 Nauk Politech. Lodz. No. 186Mat. No. 5 (1974),43-59;MR # 1 3 4 8 41. 2 , 6 , 9 , l 1 , 1 2 , 2 4 1 starlike 1473.twomey, J. B. An integrtt mean problem for bounded no' issuc 1, vcl .16, rro. functions.(Abstract),Notices,A. M. S., 1 1 1 ,J a n . ! 9 5 9 ,P . 2 6 9 .[ 3 , 6 , 2 2 , 6 2 1 Soc' 1474.Twomey, J. B. On startikefunctions. Proc' Amer' Math' 95-97;MR 40 #2843'[6, 16,62,631 24(19'10), J. London 1475. Twom ey: , J . B. On the derivativeof a stertikefunction. 53] M a r h . S o .. ( Z ) , 2 ( l g 7 ; ) . 9 9 - l l 0 ; M R 4 0 1 1 7 4 3[66., 9 , 5 8 , 6 2 , London J. 1476.Twomey, J. B. on meromorphic storlikefunctions. : { R 4 4 # 5 4 4 5 .t 3, 6 , 9 , 5 8 , 5 2 1 N { a t h .S o " . , 4 ( l 9 7 l ) , 2 3 1 - 2 3 9N Math' 1477.l'womey, J . B. On boundedstarlikefuncticns- J. Analyse 24(1971),lgl-Zc/dMR45#3689'12,3,6'7,22'561 14'18.Ulina, G. V. The rangeo.f valuesof a certainsystemof functionals in the classof schtichtfunctions with real coeJficients.(Russian) no' 3' B a s k i r .G o s . U n i v . U c e n . Z a p . V y p . 3 l ( 1 9 6 8 ) ,S e r ' M a t '

342-i50;MR 43 #7619.124,29,391 of 1479.Ullman, i. L. TIre locstion of the zeroesof the derivatives Foberpolynomials.Proc. Amer' Math' Soc' 34(1972), 422-424; MR 45 #8809.[9, 16, 53] Amer' 14E0.ulknan, J. L. An ereq theoren;for schlicht functions.

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-.;, f

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[--

254

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

TOPIC REFERENCES

Following is a list of ninety topics dealing directly with or closely relatedto the theory of univalentand p-valentfunctions.Following each topic is a list of those referencesin this B:blicgraph)' which contain '' reiults perraining-,othat topic. The toplcsare numberedl,'1,T2, T3, BibliT90. The threetopicsTl5, TlT,and r59 are nor beingusedin this ograph;'. Tl. The principte o.fSubordinatio;l(niajorization,quasi-subordination' hull-subcrdination). 136,I 37, 139,148,149', 14,42,43,50,78, 87,99, 125,133,I ?4, 13:, 188' i 5 4 , i 5 5 ,1 5 6 ,1 5 7 ,i 5 8 , l 5 9 , 1 6 1 ,1 6 2 , l & , t 6 5 , l ' 7 6 , 1 7 7 , 1 8 3 , 399,482' 202,207 ,208, 212,213,272,307,330, 335, 340,354,387, 629', 542,544,545,546,548,54g,550.551, 552.503,613, 614,615, 830' 686, 687,694,695,7M,710, 72g, 745,i 54,818,825,827,829, gl2' gM,906, 913' 910, 831, 837,839, 840,8+i, 850,8-59,892,903,

TOPIC REFERENCES

, 1 2 2 , 1 1 2 6 , 1 1 5l l0s ,2 , 1 2 1 9 , 9 1 5 ,g 2 7 ,g 4 2 , 9 5 39, 5 5 ,9 8 1 ,1 1 0 9 1 ,1404, 1224,1226,1250,1254,!322, 1325,1385,1389,1390,1391 , 5 2 6 , 1 5 2 81,5 2 9 1 1 4 0,51 4 0 7 , 1 4 6 71, 5 0 9 1 part (functionalsof positiverealprrrt). Tz. Functionsof poshive Real gl, 1 7 6 ,1 8 4 ,i 9 5 ' 2 0 3 '2, O 4 ' I l 5 , 3 2 ,3 4 ,4 2 ,4 3 , 1 0 7 ,1 4 1 ,1 4 2 ,1 4 7 , 354,376, 224,247,z's+,255,256,257,258,267,268,278, 319, 35,2, , 6 , M 8 ,M 9 , 4 5 0 ,4 5 2 , 4 5 4 , 4 5 45 5, 9 , 4 6 04' 6 2 '4, 6 3 ' , 3 8 7 ,4 ? 7 , 4 4 0M 583,584,585, 571l, 470,47g,487,4g3,4g4,522,523,542,546,551, 640,642,643,il4, 557,664'6o6'667'668'672' 588,627,628,531, , 56' 81 3 ,3 8 , 358 6 8, 1 6 , 8 4 ,7 0 3 , 7 1 6 , 7 1782, 3 , 7 2 8 , 8 2 4 , 8 3 679,68C g o 7 , g | 2 , 9 2 | , 9 2 4 , 9 2 8,950, 8 5 8 ,8 6 9 ,8 7 7 , 8 8 38,8 4 ,8 8 5 ,8 8 6 ,8 8 ? , 105J' 9 6 l , 9 6 4 ,1 0 1 0 ,1 0 1 5 ,1 0 1 6 ,1 0 3 1 ,1 0 3 3 ,1 0 4 9 ,1 0 5 0 ,1 0 5 2 , 1, 1 1 3 , 1 1 0 8 , 0 8 6 1, 0 8 7 1, 0 8 81, 1 0 5 , 1 0 7 6 1, 0 1 71, 0 7 81, 0 8 0 1, 0 8 4 1 1189, 1 1 1 9|,| 2 0 , | i 2 4 , 1 1 3 5t,1 3 9 ,1 1 4 0l,1 4 l , | | 4 4 , 1 1 4 81, 1 8 7 , |,2 8 9 , | 2 8 1 I 1 1 9 ,81 , 2 2 : r| ,2 2 8 ,| 2 3 4 , t 2 4 g ,| 2 5 0 ,| 2 5 3 ,| 2 5 6 ,1 2 5 8 , i295,1296,1298,1299,1320,l35l' 1290,l2g|, 1292,1293,1294, |420, | 3 5 2 , 1 3 5 4| 3 , 5 7 ,1 3 8 11, 3 8 71, 3 8 8|,3 9 7 ,| 4 | 5 , 1 4 1 6|,4 | 9 , 1513, | 4 2 t , | 4 3 7, | 4 4 0 ,| 4 6 3 ,| 4 6 7, | 4 7 2 ,| 4 7 7 ,1 4 8 1|,4 9 6 ,| 4 9 9 , 1 5621 1 5 5 4 ' 1 5 5 1 , 2 ,1 5 4 3 , 15191 , 520,1528,1529,1534 ,1541 T3. Integral Meons. 5l'7, 551' 567', 587', 387 [78, 87, 126,172,274,282,354,386, ,480, 1 1 2 5 ,| 1 2 6 , 7 0 6 , 8 7 4 , 9 5 6 , 1 0 ,2|10 2 7 , 1 0 3 8 ,1 0 3 9 ,1 0 4 0 ,l M 8 , 1 0 5 1 , | 523l. | 2 2 4 , | 2 2 6 , | 2 5 4 , | 3 2 0 , 1 4 3 8 ,| M , | 4 7 3 , | 4 7 6 , 1 4 7 7 , (p-valency); Trans' T4. Sufl^icient(necessary)Conditions for Univalency (J formations Preserving nivalency' [ 5 , 8 , 2 6 , 2 7 , 2 8 , 3 3 , 6 4 , 7 1 , 7 2 , 7 5 , 7 6 , 7 7 , 7 8 , 7 9 , 8 0 ' 1 0 1 ' 110920' ', 1 0 3 ' , 1 8 3 '1 8 5 ' , 1 0 8 , 1 2 4 , 1 2 6 l, 2 g , 1 3 0 ,1 3 3 , 1 4 3 , 1 4 4 , 1 4 5 , 1 7 l , 1 7 4 ' 255' 268' 273', 202, 203, 214, 217, 220, 225, 227, 245, 247, 248,252' 356',370', 281,288,28g,2g0,2g3,2g4,296,303,334,337,352'355' 4 5 1 '4 7 5 '4 7 8 '4, 7 9 ' , 3 9 3 ,3 9 5 , 4 0 7 , 4 0 g , 4 1 04, 1 3 , 4 2 4 , 4 3 6 , 4 3 7 , 4 3 9 ' 687,694, 6 4 8 0 ,4 8 9 , 4 g 5 , 5 4 2 , 5 4 9 , 5 5 2 , 5 5 4 , 5 7 5 , 660015, , 0 8 ,6 5 8 , 8 1 7 ,8 3 5 ,8 3 6 , 6 9 6 ,6 9 7 ,7 0 7 ,7 5 5 ,7 5 6 ,7 5 7 ,7 6 2 ,7 7 3 , 8 0 28, 0 5 ,8 1 5 , 9 1 0 ,9 | 4 , 9 2 8 , 9 0 8 , 8 M , 8 5 1 ,8 5 3 ,8 5 8 ,8 6 8 , 8 7 2 , 8 8 89, 0 0 ,9 0 3 ,9 0 6 , 1 0 0 4 ,1 0 1 1 ,1 0 1 4 , 9 3 3 , 9 4 6 ,9 5 6 , 9 5 8 ,9 6 6 ,9 6 9 ,9 7 1 r , 9 8 69,9 2 , 9 9 9 , 1055'1063' 1054' 1020, toz|[ 1031,1037,1040,1050,1052,1053, ll25' ll37' 1 0 8 6 ,1 0 8 8 ,1 0 9 0 ,1 0 9 5 ,l o g 7 , 1 1 0 0 ,l l l 0 , 1 1 1 3 , 1 1 2 4 , 1250,L259,|260, 1199,|22:^,|222, t223, |225, |228, |23|, |248,

h-_

I

256

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

, 2 9 7 ,1 3 0 1 ,1 3 c 4 ,1 3 0 6 ,1 3 0 7 ,1 3 0 8 ,1 3 1 0 ,1 3 1 6 '1 3 1 7 , 1 2 7 4 ,1 2 7 6 1 ,1406,1407,1414, , 3 3 5 ,1 3 5 3 , 1 3 6 71, 3 8 0 ,1 4 0 1 1 3 2 1 , 1 3 2 41, 3 2 7 1 1 4 1 7 , 1 4 2 01,4 3 8 , 1 4 4 31, 4 6 1 , 1 4 6 41, 4 6 9 , 1 4 8 61, 5 2 9 ,1 5 3 6 '1 5 3 9 , 1 5 4 ,11 5 4 3 ,1 5 4 8 1 functions), and Generalizations. T5. Close-to-Convex(linearly qccessible 1 8 1 ,1 9 4 ,1 9 5 , 1 3 4 , 4 4 , 7 88, 0 , 1 0 2 ,1 0 6 ,1 1 3, l 4 l , 1 4 2 ,1 4 3 , 1 4 4 , 1 4 5 , 2C3,2I4, 220,221,227, 248,252,273, 278, 281,292, 340,3 54, 386, 391, 436,440,442,443,446,453,456,46A,480,520,524,526,542, 7 ,0 3 , 7 4 3 , 5 4 3 ,5 4 6 , 5 . 4 85 ,5 0 ,5 5 1 , 5 7 2 , 5 8 86, 1 6 , 6 9 2 , 6 9 3 , 6 9 4 , 6 9 8 8, 6 9 ,9 0 6 . 8 6 7 , 8 6 8 8 6 6 , 8 5 5 , 7 4 7 , 7 4 8 , 8 0 2 , 8 0 38,3 5 ,8 3 6 ,8 3 7 , 8 3 8 , 1051 , 1052, 910, gl2, g28,931 , 943,950,957,999,1004,1006,1040, 1 0 5 3 ,1 0 5 5 ,1 0 5 9 ,1 0 6 0 ,1 0 6 l, 1 0 7 6 , 1 0 8 2 ,1 0 8 4 ,1 0 8 5 ,1 0 8 7 ,1 1 0 9 , , 1 3 9 ,1 1 4 2 ,1 1 4 9 , 1 1 7 81,1 8 0 ,1 1 8 4 ,1 1 9 9 , 1 2 1 9 , 1 1 1 9 ,1 1 2 0 ,1 1 2 4 1 1220,1222,1225,1231,1245,1246,1249,1250,1259,1260,1301' 1 ,4 0 0 , 73 , 3 3 ,1 3 4 0 ,1 3 5 1 ,1 3 5 3 , 1 3 8 2 , 1 3 9 7 1 3 0 4 ,1 3 2 1 , 1 3 2 3 , 1 3 2 1 1401 , 1 4 0 9 ,1 4 4 1 ,1 4 6 9 , 1 5 C 21,5 1 4 ,1 5 2 3 , 1 5 4 31, 5 4 8 ,1 5 5 9 1 T6. StartikeFunctions, Spiral-tike Functicns, and Generslizations. 1 0 1 '1 0 2 ' [ 2 0 ,3 0 , ] 3 , t 4 , 4 2 , 4 3 , 4 4 , 5 1 , 5 4 , 6 6 , 7 0 , 9 1 , 9 2 '9 3 ' 9 9 ' 1 0 3 ,1 0 6 ,l l 2 , 1 1 3 ,l l 4 , 1 1 5 ,l l 7 , 1 1 8 ,l 1 9 , 1 2 6 ,l 3 l , l 4 l , 1 4 2 ,1 4 3 , l M , 1 4 5 ,i 4 6 , 1 5 5 ,1 6 0 ,1 6 2 ,1 6 3 ,1 6 5 ,1 6 6 , 1 7 01, 7 6 , 1 7 9 , 1 8 11,8 4 ' I 85, I 88, I 9 l, I 92, Ig4, 195,I 98, 202,203,214,220,221,225,229, 230,248,253,254,257,268,269,273, 281,29l, 293,3 I 3, 314,319, 326,327,330,335, 340,342,343,344,345,347,348,349,351,352, 354,356,357,377,37g,388,391, 392,394,420,437,438,439,447, 453,455,457,458, 459,460,466,468,475,488, 489, 517, 525,526' , 4 2 ,5 4 3 ,5 M , 5 4 5 ,5 4 6 , 5 5 05, 5 1 , 5 5 2 , 5 5 35, 8 i , 5 8 2 ' 5 2 7 ,5 2 8 , 5 4 0 5 583,586,587,588, 5gg,600,601, 602,603,606, 614,615,616,619' 629,533,635,639,641, 642,543,658 665. 666,688,689, 692,693' 7'16-' 695, 697,703,70),7 12,7 13,726,727,7 45,747,748,7 52,775, 8 4 4 ,8 4 8 ' 7 7 7, 7 9 0 , 7 g 1 , 8 0 2 8 , 0 7 , 8 2 5 ,8 2 6 , 8 3 08, 3 4 ,8 3 5 ,8 3 7, 8 4 1 , 8 5 0 , 8 5 2 , 8 5 38, 5 5 ,8 5 7 ,8 5 8 ,8 6 0 ,8 6 6 ,8 6 8 ,8 7 3 ,8 7 4 , 8 8 28, 8 4 ,8 8 7 ' 92-7 8 8 8 ,8 8 9 ,8 9 1 , 8 9 2 , 8 9 3 ,g M , 9 0 6 , 9 1 2 , 9 1 3 9, 1 5 ,9 1 6 , 9 1 7 ,9 2 5 , g28,930,g41,952,957,966,968,97g,988,989, 99c,991,995,997.', ggg,1002,1009, 1012,1014,1015,1031,1036,1038,1039, I'M3' 1 0 8 3 ,l 0 q 4 ' 1051 , 1 0 5 2 , 1 0 5 3 ,1 0 5 4 ,1 0 7 1 1, 0 7 8 , 1 0 7 9 , 1 0 8 01 ,0 8 1 , 1 0 8 5 ,1 0 8 7 ,1 0 8 8 ,1 0 9 0 ,I 1 0 9 , I 1 1 3 , 1 1 1 9 ,1 1 2 0 ,1 1 2 2 ,1 1 2 3 ,l l ? : ' , 1 1 3 2 , 1 1 3 3 , 1 1 3 14 1, 4 7 , l l 4 g ,1 1 5 0 ,1 1 5 3 ,1 1 7 0 ,1 1 7 l, i \ 7 7 , l l l ? ' 1190,ll9l, 1195, 1203,1204,1205,l2lg, 1221,1224,1225,1226',

TOPIC REFERENCES

257

1250',1273' 1283' 1294', 1234,1241,1242,1245,1246,1248,!249' | 3 2 5 , | 3 2 7 , 1 3 3 0 ,1 3 3 1 ' | 2 g 7 , 1 3 0 4 ,1 3 1 9 ,| 3 2 0 , | 3 2 | , | 3 2 2 , | 3 2 3 , 1 3 5 3 ,1 3 5 6 ,1 3 5 7 ' 1 3 3 5 ,1 3 3 6 ,1 3 3 9 ,| 3 4 2 , B + q , 1 3 4 8, | 3 4 9 , 1 3 5 0 , 1 - 1 5 0 , | 3 6 2 , 1 3 7 8 , 1 3 8 3 , 1 3 8 4 , 1 3 8 5 , 1 3 8 6 , 1 3 8 7 , 1 3 9 11, |431962, , | 3 9 1 , , 4 0 8 ,| 4 0 9 , | 4 \ 0 , 1 4 1 5 , , | 4 0 2 ,! 4 0 4 ,| 4 0 , 71 1 3 9 8 ,1 4 0 0 ,1 4 0 1 1 4 1 8 , 1 4 1 9 , 1 4 2 0 , 1 4 3 7 , 1 4 4 1 , 1 M 2 , 1 M 4 ' 1 4 6 7 ' , 1 4 6 9 ' 11457221',1 4 7 3 ' , l51l, |5|2, 1514, | 4 7 4 | 4 7 5 , ! 4 , 7 6 |, 4 7 7 , | 4 8 7 , 1 5 0 0 ,1 5 1 0 , 1 5 3 8 ,1 5 4 0 ,1 5 4 1 ,| 5 4 2 , | 5 2 2 , | 5 2 6 , | 5 2 7 , 1 5 2 8 ,1 5 3 3 ,1 5 3 4 ,| 5 3 7 , 15411550,1551,1552,1553,1554'1555'!55?',1558'15601 T7. Length of Imoge Curve' [51,17g,204,225,278,287,310,311'?24'?49',350'376',480',620', 6 5 0 , 6 8 9 , 8 4 9 , 8 6 3 , 8 7 4 , g 5 2 , g 5 7 , g 7 4 ' 9 8 1 ' , 1 0 3 9 ' , 1 0 5 1l$s ',1054',1055' 1320',1392',l44l ', 14r',2', ' 1086, I 128, ll4g, 1180, 1234, 1235' 1477, 1487) TE. CoefficientBoutidsfor I\on*t I

- lont

[81,359,362,376,466,468,609'649'881',945',1040',1047',1153', 1155,1220,15431 T9. Meromorphic (JnivarentFunctions Convex, Close-to-Convex'etc'

(functionars),incrudingstarlike,

1 2 8 '1, 3 4 ' 1, 3 6 '1, 7 6 '2, 3 0 '2, 3 3 ' , 91 [ 1 , 8 , 2 7, 6 8 , 1 1 , 7 2 , ' , 1 8 , , 9 6 , 1 0 4 ' 243,265,27g,282,296,'314,315'316'317',331',333',340',421',129', 441,457,478,489,490',506,524'535'583',621 ',647',650',652',664' 7 51',757',759'764', 149',750', 727' 776:' 722:, 13, i 12, 7 709, 708, 688, 8 5 7 '8, 6 7 ' 8 7 7' , 9 3 49' ,3 5 '9, 3 8 ' , 77|,7g!,796,797,8148 ; 23,842'843' 1076'1078' g3g,g40,gM,950, g5r: g52,g54'966'1002'1035'1043', |0,7g,1080,1081,1083,1094,|||2,1113,1130,1131,1141,1151, 1155,1158,i170,||7|',|234,t241,|242,|243,|261,t278,|289, |2g|,|2g5,|296,|332,1351,|357,1358,|?94,|4|9,|420,|436' 1 4 4 5 , 1 M 6 , 1 4 4 7 , 1 4 4 9 , 1 4 5 0 , 1 4 5 1 ' 1 4 5 2 ' , 1 4 5 3 ' ,1520, 1 4 5 41522' ',1455',1456', l47g' 1519, 1476' 1475, 1472,, 1466:, 1461, 1457,1459, 1535,1536,153i,1546,1547'1549'1550',15521 Tl0.ConvexFunctions(andgeneralizations). 14,20,30,33,34,54,"1!,72'gl'gg'102'106',125',139',141',142' 143.144,145,147,155,161,162'165'166',176',179',180',183',188', |g4,|g5,20,2,2|2,2|4.,22|,227,23|,232,24,7,248,252,254,259,

25E

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

261,264,266,268,269,272, 273, 29l, 293,324,326,340,342, 3 46, 350,352,354,376,378,386,388,397,399,453,455,457,460,473, 475,479,518,526,542,543,54A,551,552,568,570,619,633,634, 6 8 7 ,6 9 3 ,6 9 5 ,6 9 8 ,7 0 3 ,7 M , 7 1 2 ,7 4 5 ,7 4 8 ,7 9 5 ,8 1 7 ,8 3 4 ,8 3 6 ,g 4 l , 8 5 5 ,8 5 9 ,8 6 6 ,g 6 g ,8 9 l , 8 9 3 ,8 9 5 ,W , 9 0 5 , 9 0 6 ,9 1 0 ,9 1 2 , 9 1 3g, l 5 , 9 2 5 ,9 2 7 , 9 2 8 , 9 5 5 ,9 5 7 , 9 6 8 ,9 8 8 ,9 9 0 ,9 9 1 , 9 9 3 , 9 9 7 , 9 9 9 ,1 0 3 1 , 1 0 3 6 ,1 0 3 8 ,1 0 3 9 ,1 0 4 0 ,1 0 5 0 ,1 0 5 1 ,1 0 5 2 ,1 0 5 3 ,1 0 5 4 ,1 0 5 5 ,1 0 6 1 , 1577,1078,1084,1085,1087,1089,1090,I I 13, 1I lg, I 120, 1122, 1 1 2 1 ,1 1 3 9 ,1 1 8 9 ,1 1 9 0 ,1 2 0 4 ,l 2 l g , 1 2 2 1 , 1 2 2 5 , 1 2 2 61, 2 2 7 , 1 2 3 4 , 1244,1245,1246,1248,1250,1259,1273,1282,1294,1297,l3lg, 1 3 2 0 , 1 3 2 r , 1 3 2 3 , 1 3 3 2 , 1 3 i3333, 5 , 1 3 3 6 ,1 3 3 9 ,1 3 3 9 ,1 3 4 7 ,1 3 5 3 , 1 3 8 5 ,1 3 8 6 ,1 3 9 2 ,1 3 9 6 ,1 3 9 9 , 1 4 0 0l ,4 0 l , l 4 M , 1 4 0 5 , 1 4 0 7 , 1 4 1 2 , 1 4 1 8 , 1 4 2 0 , 1 4 6 9 , 1 4 7 0 , 1 419511, 2 ,1 5 1 4 ,1 5 3 4 1 , 5 4 1 ,1 5 4 5 ,1 5 5 9 , 15611 Tl l. Radiusof Slarlikeness(of various classesof functions). 1 3 0 , 3 2 , 3 4 , 9 1 , 9 2 , 9 4 , 9 51,0 0 ,1 0 3 ,1 0 5 ,1 0 6 ,1 1 4 ,I 1 9 , 1 2 3 ,1 4 5 , 147,205,214,224,229,247,253,254,257,267,287,298,376, 437, 438, 439,447,449.451,453,454,457,458,460,487,497,5 16,522, 5 2 7 , 6 1 96, 3 5 .6 3 9 ,6 4 1 ,& 2 , 6 5 5 ,6 6 6 ,6 6 9 ,6 9 9 ,7 1 4 ,1 2 8 ,8 5 5 .8 6 8 . 8 7 3 , 8 8 2 , 9 8 7 , 9 8 8 , 9 8190, 1 4 1 , 0161 , 0 3 3 , 1 0 7 61,0 7 7 1 , 0 7 8 ,1 0 8 1 , 1 0 8 4 ,1 0 8 7 ,1 0 9 0 ,1 1 2 4 ,1 1 3 4 ,I 1 8 7 ,1 1 8 9 ,1 l 9 E, 1 2 2 7 , 1 2 4 2 ,1 2 5 1 , 1262,1289,1293,1294, 1295,1297,1298,1299,1335,1338,1350, 1352,i357, 1361,1381,1386,1387, 1396,1467, i472, 1487,l5l l, 1526,I 528, I 533, 1542,l5M, I 553, I 5551

Tl2. Radiusof Convexity(of various classesof functicns). [32, 33, 35, 73, 91, 93, lffi, i03, 106,ll7, 123,142,211,212,214, 220,225,239,24i . 255,267,268,289,292,330,3,10,349, 35i, 374, 3 7 6 , 3 7 ,73 8 0 ,3 8 1 ,4 4 0 ,4 4 1 .4 4 2 ,M 3 , M 6 , M 9 , 4 5 1 ,4 > 3 , 4 5 i ,+ 6 0 , 5 2 6 , 5 2 ,75 4 2 , 5 4 4 , 5 7 2 , 6 1 56,1 9 ,6 3 5 ,6 4 0 . 6 4 2&, 3 , f f i , 6 5 7 , 6 5 8 , 6 6 7 , 6 6 87, 0 2 ,7 2 6 ,7 2 7 , 7 6 5 7, 7 6 ,7 9 5 , 8 0 58, 5 5 ,8 5 8 ,8 6 8 ,8 8 2 ,8 8 4 , 895, 887, 888, 889,905, 921, 924, 926,930, 93I , 950, 966, 967, 969, 9 8 4 , 9 8 7 , 9 8 89, 9 0 ,9 9 6 , 1 0 0 2 1, C 0 91, 0 1 0 ,l 0 l 4 , 1 0 1 5 ,1 0 1 8 ,1 0 3 3 , l c 6 l . 1 0 7 9 ,1 0 8 1 1 , 0 8 3 ,1 0 8 4 ,1 c 8 6 ,1 0 9 0 ,| 1 2 4 ,1 1 3 5 ,1 1 3 9 ,I l 4 l , Ll44,l187, I190, I196, I198, 1235,1242,1249,1251,1257,1260, 1289,1291,1292, 1294,1295,1296,1297,1318,1333,1335,1338, 1 3 4 6 , 1 3 4 81,3 4 9 , 1 3 5 0l J, 5 1, 1 3 5 2 , 1 3 5 7 , 1 3 8 11,3 8 6 ,1 3 E 7 , 1 3 9 6 , 1 4 i 6 , 1 4 3 7 ,i 4 6 j , 1 4 7 i . 1 1 7 2 ^1 1 8 7 ,1 5 1 9 , 1 5 2 0 , 1 5 2 '1, t5, 3 3 , 1 5 3 4 , 1 5 3 5 ,1 5 3 8 ,1 5 4 3 , 1 5 4 6 ,1 5 4 8 ,l 5 _ s 01, 5 5 2 1

r ,". 1"s ':

13

',il

TOPIC REFERENCES

259

Tl3.Typicolty.rea|Frunctiorrs(andgeneralizations). 1 4 2 , 4 3 , 9 1 , 1 5 1 , 1 7 8 , 1 g 7 , 2 6 7 ' 3702',705', 0 0 ' 3 0 11' , 3 1 9 ' 3819', 2 5 ' ,820' 366',382'4M', i, 628'512'583' 546,55 \?:725' 47l, 521,, 465, g?g'1005'1118' 1148'1204't207'l'224'122i' g2(1', 821, 8'79,904, 15571 , neq' 15M' 1540', , l'247,1258 1236,1237 ond Generalizations' T 14. P-volent(weaklyp-valent), 427' 453, 466,468, 475, 482, 3',77 ' ' 364,36',7 I03 ,246,282,28?, 653, u, , 5 8 '5 5 9 '5 6 2 '564,56i, 599,600, s i l , 5 3 8 ,5 1 ,' 75 4 8 ,5 4 9 ,5 5 0 5 976,977,978, '713,714,797,803, 804,805,807',866',867'E 6 9 , 8 7 8 , loSo'1 0 8 7 1, 1 0 3 1, 1 8 7 1, 1 9 9 , 1c06,rooo,lo3o, 1042,lo44,lo5o' 1398, ', 1375' 1 3 8 0 1, J 8 1, 1 3 9 ' 7 , , 1294,1343, 1373 i226:,n4l , 1255 I5361 1484,1485' 1486' 1 4 8 7 I, 5 0 8 , I 5 2 8 ,

, , 1420 tigg,1 400, 1413

(This topic is not being usec') Tl5. Distortion Theorerts T16. Coniectures,OPenProbletns' 1 1 g , 7 8 , 8 7 , 1 0 2 , 1 1 2 , 1 1 7 ' 1 7 739^5-,398' ' 1 8 7 ' 2 0405' 0 ' , 2 1 4 ' 2459' 1 5 '473', 2 5 2 474', '268',278', {q' 2gg,330,335,336,n;,aM,355' 613', 606', 603', ', 59-1', 550',55'7 542'146^'', ,482, 484"12'+' 475,476,4'77 g + s ' 8 6 8 ' , 8 7' ,18 ' , 7848' 9' , 9 C 4 ' , 819' 6 1 9 , 6 2 0 , 7 0 4 , 7 4 5 , 7 4 6 "8a108r '' ' ll24' 1109'1113 1079', gg2'1020-', 1054', 905,906, 914,956,96;' l z l g ' \ z } a ' l 2 2 l ' 1 2 2 41, 2 2 6 ' 1 1 3 11 1 53 , 1 1 6 4 , 1 l d, l l 7 l , 1 2 0 0 , ', 1304',1320',1323',1325',132'7 1279', 1228,1241,1242,124;"n54' 1 4 0 21' 4 4 41' 4 4 61' 4 7 4 , 1 4 7 9 ' t 3 2 g1, 3 3 51. 3 5 01, 3 5 i ,i l g r , r + o o, 1 5 3 01, 5 5 7 j (This topic is not beingused.) Tl7 . CoeJficientBourrds T18. Area of Image Domain'

6',M 0 , M 6 , 4 8 C ,5 8 3 ,5 8 6 , \72,,2M, 225,261,3I 1' 355',3',7 163,162, 9 8 1 '1, 0 3 9 1, 0 5 1 , 1 0 5 41 ,0 5 5 , '78',7 z g o , , 7 8 9 ,8 6 3 ,8 7 3 ,8 7 4 , 9 7 4 ' 9 7 9 ' 1086,1149,1254,l44l, 14871

values,KoebeSets,Bloch'sconstant). (m\ssed T 1 9 . CoveringTheorems

[1,18,19,20,11'7,143,1M,145,152'153',163'178'201',212',260', 2 6 2 , 2 6 3 , 2 6 6 , 2 g 1 , 3 0 5 , 3 0 6 , 3 1 3 ' 3 3745', 5 ' , 3747', 7 6 748', ' , 3 9790', 1 ' , 4791' 40'493',507',513' 7 ll',7 12', .650;685,686,68',7' 57l, 642,647 793,826,832,834,883,889,891'900',903',g27',958',97',7',978',980

260

B IBL IOGR AP H YOF S C H LIC H T FU N C TION S

1020,t021,1023,t024,1025,t026, I104, 1124,1126,tt62,r164, , 301, 1201,1203,1205,1206,1 2 1 2 ,1 2 1 6 ,l2l7 , 1243,1262,t 2 9 2 1 1 3 3 3 , 1 3 31347, 5 , 1348,1 3 7 6 ,1 3 8 4 ,1 3 8 6 ,1 4 0 2 1, 4 1 1 ,t413,1429, l48g 1469 1482, , 1492,1497,1498,1 5 2 7 , 1 5 3 9 1 , T20. Partial Sums(Cesiro sums). [3, 125,139,r47, 193,2m, 2M, 436,442,+47, 448,451,452,540, , 087, 6 3 5 ,6 8 7 , 6 9 06, 9 1 ,7 2 0 , 7 4 6 , 7 5 3 , 8 3 6 , 9 1 0 , 9 1130,6 0 ,1 0 7 6 1 15291 1487 1352, 1323, 125A, n2l, 1222,1,244,1249, , T2l. Coefficient Bounds (relations) -fo, Functions (functionats) of Positwe Real Part of Topic 2 . [15, 107,125,139,147,2M, 436,450,459,462,540,542,571,585, 5 8 8 ,6 2 7 ,6 2 8 ,6 2 9 , 6 3 5 ,6 4 0 ,6 4 2 ,6 5 7 , 7 4 68, 2 4 ,8 6 9 ,8 8 3 ,8 8 5 ,8 8 7 , 9 0 7 , 9 1 0 , 9 1 3 , 1 0 8 6 ,1 0 8 7 ,I 1 8 7 , 1 2 2 2 ,1 2 4 9 ,1 2 5 0 ,1 2 5 6 ,1 2 8 1 , 1323,1352,1415,1467,15i31 T22. BoundedFunctions (functionals). 1 4 , 3 1 , 3 25 , 9 , 9 1 .I I ! , I 1 5 , 1 2 5 ,1 2 7 ,1 3 0 ,1 5 4 ,1 5 6 ,1 6 6 ,1 7 0 ,1 7 9 , 180, 2 \3 , 236, 237, 238, 265, 216 ,28 I , 295, 297, 305, 306, 307, 30E, 3 0 9 ,3 2 3 , 3 4 1 , 3 5 13,5 3 ,3 5 3 ,3 8 4 ,3 8 5 ,3 8 8 ,4 1 8 .4 3 0 ,4 3 1 , 4 3 2 , 4 3 3 , 134,438,450,453,496,497,507,522,536,588,605,621,622,624, 625,626,661,693,704,732,733,i34, 798,800,801,846,854,856, 883, 891, 895, 904, 919, 927, 936, 937,938, 962, 963, 971, 1050, 1 0 5 2 ,1 0 7 8, 1 0 9 2 ,I 1 2 8 ,1 1 5 5 ,I 1 6 3 , I 1 6 5, 1 1 7 3 ,1 1 8 7 ,1 2 0 1 ,1 2 0 3 , 1205,1209,1210,l2ll, 1229,1233,1242,1249,1251,t253, 1262, 1264,1271,\272, 1275,1276,1277,1290,1296,1298,1306, l40l, 1329,1347, 1354,1356,1357, 1367,1368,1369,1375,1381,"328, 1402,1418,1422,1423,1424,t425, 1426,1427,1443,1473,1477, 1 5 1 6 ,1 5 2 8 ,1 5 1 2 i, 5 6 0 1 T23. RepresentationTheorems(formulas). [ 4 1 , 1 3 0 l, 5 l , 1 7 8 ,1 8 4 .1 8 7 ,l 9 l , 1 9 2 , 2 7 3 , 2 7 82 ,8 8 ,2 9 3 , 3 \ 9 , 3 2 5 , 3 4 0 ,3 4 7 ,3 5 2 , 3 5 53, 8 2 ,4 0 9 ,M 5 , 4 6 5 ,4 6 9 , 4 8 14, 8 3 ,5 1 3 ,. 5 1 65, 4 2 , 5 4 6 , 5 5 15, 8 1 ,5 8 3 ,5 8 5 ,6 6 0 ,6 8 1 ,7 0 7 , 7 7 9 , 8 0 28,0 8 ,8 1 9 ,8 7 2 ,8 7 3 , 874, 879, 892, l0l I , 1012,1014, 1034, 1035, 1039,lM0, 1043, 1 0 8 0 ,1 0 8 3 ,1 0 8 8 ,11 0 5 ,11 0 6 ,l l 1 3 , 111 8 , l l 1 9 , 1 1 2 0 ,1 1 2 3 ,1 1 2 4 , 1125,I 138,I 153, 1207,1234,1256,1273,1327,1335,1342,134?, 1 3 4 8 ,1 3 8 2 ,1 3 8 5 ,1 3 8 6 ,1 3 6 7 ,1 3 9 7 l, 4 S , l 4 0 l , 1 4 1 9 , 1 4 9 11, 5 0 2 , 1 5 1 0 ,l 5 l I , 1 5 2 0 ,1 5 2 7 ,1 5 4 0 ,1 5 4 8, 1 5 5 4 ,1 5 6 0 1

TOPIC REFERENCES

261

Methods' T?A. Variationai(symmetrization) 55' 56',68',82',83',84',87',89',90', [18,19, 37,42,44,45,46,52,53, i i l . l ! 5 , 1 3 1 , 1 3 3 , 1 3 1 , 1 5 2 , 1 6 7 ' 1 6 8 ' 1 6 9 ' 1 8 4395', ' l ? l ' 2 3 042r', ',235'238' 391',392', 408', 3n:,313'341'342', 250,251,287,288,3U6; 498',500',530',532',569',576', 422,474,425,426,$2:, 434,485'486' 645 648', 651',661', 662',672' 601,601 , 612,626,633;$6:,638' 642:', ', 49,7 52,758, 7 60,769,792,808' 74|, 7 42,,.1 676, 7 03,7 07,7 33,7 34,, 896', 895', 860;875'!78',890',892',!?3'894', 842,843; 813,831,833, gl 98r', 938'gll'95i', g54' >' 976',982', 891,gl4, g20,g23,934"935: l 1 0 5 5 1, 0 5 8i,1 0 5 ,1 t 0 7 , l 0 E , 9 8 5 ,1 0 0 71, 0 i 2 ,1 0 1 3 |, 0, 2 5 , r c i a e . | | | 2 , 1 1 1 3 , 1 1 1 5 , 1 1 2 0 , t | 2 | , | | 2 2 , 1 | 2 3 , 1 112c6', 3 0 , 1!1209 3 1' ,1212', 1138,||,46, 1205 ' 1201' 1l?5' fi73' 1170; 161, i 1150,1152, 1225,1256,1266,1269,1271'1273'1274',1276',1341',13M'1383' 1432,1472,1478,15021 univalentFunc' Bounds(relations)for Meromorphic T25. coefficient 'toPic 9 ' tions of U 7 6 , 2 6 5 , 2 9 6 , 3 1 4 ' 3 1 5 ' 3 1 6 ' 3 3 18'8333g ' 5' C t 64' 3 51'8038' 6014' 174' 616' 4 ' 6 8 8 ' ,1 0 '3, M 7 0 8 ,7 1 2 , 7 4 9 , 7 5l0i t,, 7 6 4 ' 7 7 1 '8 4 3 ' , l4/ts',t 146',15221 1170,1171, 1234,l27g:,n3;',2'l4lg', (imagedomainshaveno common T26. (Jnrelated(di.sioint)Functions values). u5,59,60,88,89,90,196'308'512'514',515'6/'6',651',73t',811', 8I 6, 1019, i 42ll T27, Are,l Principle(and generalizations). 1 g , 6 2 , 2 6 5 , 2 8 2g, 2 , ',589',611' '5, 01250' 1,' 5135431' 3- 5688' 134' ,2538' 7 i +9, 6 , 3 3 8 ' 4 8 1 ' 591416'1 6 4 7 , 6 5 6 , 8 1 0 , 8 l l , a i o ' 8 2 3 '8 4 5 ' , 1480,15241 (suchas Besselfunctions'or of Functions speciat of univalence T28. functionshavingsPecialforms)' I24,25,121,322,469,675'700'701',?88',989'1016',1300',1M7' 1457.1458,14661 T29. RegionofVariabitity(ofcoefficients,orofcertainfunctionals). g2,1g7,237,238',240',242' 146,47,48, 49, 54, 6 8 , 1 6 0 , i ' 7 1 , i g \ , 1470, 47| ,485' 525', 528', 623', 467, 465 , 42g ,430, 2M,314,319,373,

262

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

6 3 6 ,6 3 7, 6 3 8 ,6 4 7, 6 6 1 ,6 8 3 ,7 2 5 , 7 3 3 , 7 3 4 , 7 4 1 , 7 4 9, 873787,8 4 2 , 1105, lcp.z,1024,1026,1049,1058, 886,921,936,937,946,982, 1 2 0 8 ,1209, l z 0 / , 1 1 1 4I,l 1 6 , I 1 3 0 ,I 1 4 8 ,1 1 7 3 , 1 1 7 14 1, 9 7 , 1 2 0 2 , 1210,l2ll, 1250,1259,13M, 1350,1355,1370,1371,1379,1382, 1 3 9 41, 4 7 8l,5 l l , 1 51 7 ,1 5 2 11, 5 4 81, 5 4 9 1 T30. Coefficient Bounds (relations)for Bounded Functions of Topic 22. 1127,170,180,281, 305, 306, 309, 358, 431,450, 536,588,624, 5 2 5 , 6 9 3 , 7 3 2 , 8 0 0 ,8 0 1 , 9 0 4 , 9 2 7 , 9 7 1 , 1 0 9 2 ,1 1 5 5 ,! 1 8 7 , 1 2 5 1 , 1271,1272,1275.1276,1277,1306,1328,1329,1368,1402,1418, 1422,1423, 1124,1425,1426,1.532! T3l. SchworzianDerivative, the Differential Equation w" * Qw 0. [8, I 3, 72, 78, I 35,227, 228,2o5,268,274, 334,337,370, 407,495, , 9 7, 9 8 4 , 9 8 7, 1 0 1 4 ,1 0 1 9 , 5 1 2 , 5 5 5 6, 9 6 , 7 6 2 , 7 7 38, \ 1, 8 2 3 , 8 5 8 8 105C,1052,1063,1090,1221,1304,1486,1494,15431 T32. Univalenceof Polynomlals(Schild, Remak, Hurwitz). u 2 2 , l z ' J , 1 2 4 ,1 7 l , 1 7 4 , 2 4 9 , 2 9 4 , 3 7 2 , 4 3 5 , 4 7 31,8 4 , 5 8 0 ,5 8 4 , 593, 659,746,799,830,910,919,929,932,1062,1091,I I 17, l'^45' 1183,1185,1186,1187, 1236,1237,1238,1239,:241, 1242,1252, 1 2 8 5 ,1 3 1 7 ,1 3 3 5 ,1 3 6 6 ,1 4 0 3 ,1 4 0 6 ,1 4 0 8 ,l n 9 , l 4 2 l l T33. Mean-valentFunctions (and generalizations). 86 , 2 , 3 6 4 , 3 6 65, 5 8 ,5 6 0 ,5 6 1 ,5 6 2 , n, 6, 7, 132,210,212,282,353 9 7 6 , 9 7 8 , l M z , 1 0 4 4 , 1 0 4, 5l M 6 , 8 8 0 , 8 8 1 , 6 5 4 , 8 7 8 , 6 5 3 , 5 6 3 ,5 6 5 , 1 0 4 7 ,1 0 5 1 ,11 5 3 ,11 5 5 ,1 3 0 3 ,1 3 0 4 ,1 3 7 6 1 T34 Bieberbach-Ei!enbergFunctions (generalizations and related classes;Grrelferfunctions;Aharonov pairs, etc.) 5 ,0 q ,5 i l , 5 1 2 , 5 1 56, 0 5 , 6 0 8 ' [ 9 , 1 1 ,i 5 , 1 8 ,8 8 , 1 3 8 , 2 6 2 . 3 0 7 , 3 0 8 646,651,1020,1021,11,J0,14931

T35. Curvsiure.LevelCurves. u 8 , 5 4 , 6 5 , 2 3 53, 5 0 ,3 7 4 , 3 7 5 , 3 7 83,8 0 ,3 9 8 ,4 1 2 ,4 7 3 ,4 7 4 , 5 0 E ' 620,659,682,895,9I 8, 921,957,972,973, 991, 520,525,528,539, 8372, ,1 1 0 4 1I,1 0 6 ,l l 2 7 , l 1 3 5 ,I 1 4 3, i 1 4 4 ,1 2 7 31, 2 8 61, 2 8 7 , 1 2 8 1551,lst9rl 1 3 9 J1, 3 9 5 , "171,

.d

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263

of ropic 6' (reretions) for startikeFunctions T36. coefficientBounds 602 [ 7 0 , 1 0 1 , 1 1 8 , 1 2 6 , 1 qSg, 6 3 , 488. 1 7 0 S1S ' 1 7 6S+0,, ' ! 7 g553 ' 1 8 8 ' l 9587 l ' 1'9601 2 ' 2' 5 3 '', 2 8 1 ' 3 4 3 ' , , 4SS :58!; ,458, 347 ,348, 345 , 6 2 9 , 6 5 8 , 5 8 8 , 6 9 3 , 7 1 2 , 7 7 6 , 8 5 2 ' 8|5277'3, 8,18370' 181,8381' ,9?1,M 3 3' ,01,c r O 9 ' , 1 0 8 7 ' 1 1 7,1| 2 4 8 , | | 2 2 , | | 3 2 , 1 1 3,3 | i 1 q , l 1 7 0 , 1418, 1 3 8 7t'+ o z , l 4 1 51, 4 1 6|,4 | 7 , 1 3 3 11, 3 3 51, 3 4 8|,3 4 g , 1 3 5 6 , ' i5431 1467,1510,151I, 1522'1527 Lemma(andgeneralizations)' T37. schwarz's 1186'12541 [388,482,1085, convexFunctionsof TopicI0' (relations) for Bounds T38. coefficient t 1 4 3 , 1 4 4 , 1 4 5 , 2 8 1 , 3 4 6 ' 61470', 9 3 ' 714911 12',867',904',1122'1220'1248' , l4l7' 1418' 1273,1319,1335 (suchas gaps'realness'rnonocoefficients on conditions special T39. tonicitY,etc')' 244'248'364' 237 201,214,236, 150, 53, :2?|'240;2!):24,2' U2, 558'624',625', &g,+ro' +g5'489',46',4gl',4g2'5-42' 834',85I' 373,376,395, 805', 7 84',790', 'llg7 7'91', 7 33,7 34,7 47"7 5l' 7 52',7 83'', 663,684, ' 12'71'12'78' ', 1265 ttry',--tigz' g37 irss ' ,1056, 908, 886, 1305,1313,1314,1118'1335'i359'1439',1478',15251 T40.FunctionswhichareStartikeinoneDirection. ' 13011 1524,642,853,1297 in OneDi;ection' T41. Functionswhichore Convex 8 3 4 '8 5 3 ' , 8 ' , - u L7' ,4 7 ' , 5 4 2 '5 7 1 ' ^ l ? ' , 5 7 56' 2 5 2 4 ' 5 1 3 , 3 N , u13, l2g7' 1301'14191 1235', ,121;'1zzo' 1223' 926,1203,1205 (la" I s n)' Coniecture T42.Bieberbach u 2 , 1 4 , 4 5 , 8 7 , 1 6 7 ' 1 6 8 '424',' 1 8 7 'qis', 3 3 3q2s',485', ' 3 3 6 ' , 35310', 9 ' 550', , - 3 3593', 9 ' , 3594' 40',359',360', 423' 422' 421' 408, 405, 395, 1068' 1067' 1065', gzl' lnz0',1064', 610, 649,655,724'-767'9M', 1200, l ,d i , | 0 g 7 ,1 0 9 81- ,1 0 01, 1 0 1 , | 0 1 4 , 1 0 7 5 1 0 7 3 , 1 0 7 0 , 1069, 1483' t265"1304;1315' 1325'lM' rzrg, tzzl, tz26,1zsoi,l24g' 15081

2M

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

T43. Radiusof Univalency(p-valency)(of various classesof functions). ',206, 2r2, [30, 3 l, 32, 54, 103, 116, 119, 122, 142, 146,178,205, 437, 438, 436, 428, l, 39 340, 214,224,228,253,256,257,288, 293, ,720448,449,454,460,475,478,482,522,5M, 572,699,702,707 1 0 7 8 ,1 0 8 1 , l 0 ' t 7 , 1 0 7 6 , 1 0 5 2 , 1 0 5 0 , 7 4 6 , 7 5 3 , 8 2 88, 8 2 , 9 1 0 ,1 0 1 6 , 1087,1088, 1094,1163,1189,1198,1227, 1241,1242,1244,1249, 1 2 6 41 , 2 9 8 1, 3 0 4 ,1 3 0 5 ,1 3 0 7 ,1 3 1 4 ,1 3 1 7 , 1 3 1 81,3 8 1 ,1 3 8 8 , l M 7 , 1448,1M9,1450,1451,1452,L453,1454,1455, 1456,1457,1459, 1460,l16i, \462,1453,1485,1503, 1528,L529,1555] T/g. SurveyArticles, Books, Cotlections of Various Papers, Symposiums, BibliograPhies. 371, 1 2 2 , 3 84, 1, 5 7 , 6 1 ,8 5 , E 6 , 1 4 0 ,1 7 5 , 2 1 4 , 2 2 6 , 2 8 02,8 5 , 3 3 3 , 7 9 4 , 948, 4 1 1 , 4 r 4 , 4 6 4 , 4 7 6 , 5 1595,6 ,5 5 7, 5 5 9 ,5 6 3 ,7 8 6 , 7 8 ,77 8 9 , 1017,1082,1162,1167,l168, 1232,1263,1268,1280,1283,1304, 1326,14901 T45. Od(i UnivslentFunctions (classS or classE) , 3 C ) , 3 3 6 , 3 3 9 ,3 8 8 , 4 0 5 ,4 2 6 ,M 9 , 4 5 8 , 5 2 4 , [ 1 2 8 ,2 5 2 , 2 6 9 , 2 9 1 546,747,802, 896, gO4,972,1c20,1040,1155,1200,1325,1339, I 4001 T46. Invariant (angular, sphericcl) Derivative. 1279,507, 876, 894, I 163, 1507J T47. Convolution.(Flrttung) of Functions. Hadamard Product. 926,955' 14, 102,116, I 39, 272,300,302,M, 450, 573,729,9C5, . 5 l , 1 3 2 5 ,l 4 0 l , 1 4 0 9 , 1 5 3 6 j 1 a 3 2 \, 2 4 5 , 1 2 4 6 ,1 2 4 9 , 1 2 5 0l 2 T48. Schticht (or other properties) in an Annulus1008' 12,150, 327, 470, 471, 730, 770, 792,894, 895, 976, 978, 1 5 5 6 1 , 1 4 8 , 1 3 6 4 1, 3 7 3 , 1 3 7 41, 4 2 8 ,1 4 j 4 , 1 4 6 7 , 1 1 3 6 ,1 1 4 7 1 T1g. SpecialGeometry of Map (such as k-fold symmetry). , 5 3 ,1 7 0 , 1 g g , 2 2 1 , 2 4 5 , 2 9 1 , 2 9 5 . 2 9 9 , 3 0381,7 ' I 4 0 ,4 7 , 5 4 , 1 1 0 1 , 2 , 5 1 3 , 5 1 6 ,5 2 1 , 5 3 15, 1 9 ' 3 4 0 ,3 6 3 , 3 9 13, g 4 ,3 g 7 ,4 3 1 ,4 3 2 ,4 3 3 M 6 2 2 ,6 7 3 ,6 9 4 ,7 4 4 ,7 4 5 ,7 4 7 ,7 7 4 , 7 8 1 7, 8 2 , 7 8 58, 3 8 ,8 5 3 ,8 6 5 ,9 0 1 ' 9 0 3 , 9 1 4 , g 3 4 , , 9 3 g5 3, g , 9 4 , g 5 7 , 9 7 4 , 9 g 7 , 1 0 3 41,0 4 0 ,1 0 9 3, 1 1 7 7' , , 5 5 4 ,1 5 5 9 1 1 2 1 3 , 1 2 5 4 , 1 2 5154, 3 5 , 1 4 3 71, 5 3 5 , 1 5 3 71, 5 5 1 1

TOPIC REFERENCES

26s

p-valentFunctionscf Topic 14' T50. coefficient Bounds (reldiioits)for 869, 1103' 15081 1282,550,670,803,807, 866, Tvpicatil'-RealF-unctionscf T51. Coefficient Bounds (reiations)Jor Topic 13. [151,628,819,820,821,9M,1207,1236'1237',12471 odd u riivotent Functions o'f T 52 coeffi,'ient Bounds (relatians)foi' ToPic 45. t405, 426,9M, lL'721 T53.FgberPolynotnigls(Grunskycoefficients). [ 1 0 , 1 3 , 2 9 , 1 3 6 , 2 9 6 , 3 0 4 , 3 0 6 , 3 0 7 ' 3 0 68 0' 350'6,90' 8 3 '36, 11 'l,' ,369137' ',6, 31985' ,' , 3 9 6 ' , 4 0 6 , 4 2,14 2 2 , 4 2 4 , 4 2 5 , 4 8 3 , a g i g , 5 8 9 , 5 9 0 ' 655,676,677,721,737,749,762,768'770'798',811',8r2',814',816', 8 2 4 , 8 4 5 , 8 5 4 , 8 g 7 , g 4 g , 1 0 2 0 , 1 0 6 4 ' 1 C 6 5 ' 1 0 6 7 ' , 1 0 6 l8l'5, 1l ,0 6 9 ' , 1 0 7 0 ' 1 0 9 6 |, 0 9 , 71, 1 0 0 ,| | 2 3 , 1 0 7 3 |, 0 7 4 , 1 0 7 5|,0 g 2 , 1 0 9 3 1, 0 9 5 , , 369, | 2 7 , 7|,3 6 7 ,1 3 6 8 1 1 1 6 0 |, 2 3 0 ,| 2 6 9 ,| 2 7 0 . ! 2 7 2 ,| 2 7 5 ,| 2 7 6 , 1 4 2 3 , 1 4 7 9 , 1 4 9 l55,l 5 l Functions of the Class S" T54. Coefficient Bounds (relations) -for f(z)_-;io,,'+...AnalyticandUnivalentinlzl< [13,14,21,49,6',7,107,108,113'l2g'l5z'1 6 7 ' , 1 6 9 ' 1 ' ,4 7 15 9' ,'2 r 2 ' , 2 4 3 ' n ,2 : , 3 3 3 , 3 3 8 , 3 5 93' 5 0 '3 9 1 '3, 9 5 ' 3, 9 6 ' , 4 0 5 ' , 277,281,306,308 504' 4gl, 4g3' 498' 499' 500' 501' 5A2'503' 422,425,445,485,48;6', 647 623',625',630', ',648',649', 505,506,509,554,589;594,601'611' 6 5 5 , 6 5 6 , 6 7 3 , 6 7 4 , 6 8 5 , 6 9 3 , 7 3 5 ' 7 4 9 ' 7 7 1 ' 8 1 1 ' , 8 2 2 ' , 1068, 829',845',865' ' g03,g04, gl4,g44,looa, rciaL 1056,1064,1065,1066,106'7 1069,1070,1071,|072,|073,|074,1075,1095,1096,|097,1154, , 3 0 6 '1 3 6 5' 1 4 0 2 '1 5 1 8 1 1 1 5 5 ,1 1 5 6 ,1 1 7 0 ,1 2 2 6 ;1, 2 7 0 ,1 2 7 2 1 Functions)'[None] T55. ContinuedFractions(appliedto Schlicht of positiveReal Part of ropic 2' T56. Distortion TheoremsJor Functictns [ 3 3 , 9 1 , 1 4 7 , 2 2 4 , 2 5 6 , 2 6 5 , 2 ' 6 ' , 7 ' 2 6 8 ' 723', 3 7 6 ' 3 8 7 ' , 4 5883', 0 ' 5 2885', 2',523',524', '679''680', 831',833', 542,62'1 ,631, 640,643,644,651 8 8 7 , g | 2 , 9 5 0 , 1 0 5 0 , | 0 7 6 , 1 0 7 8 , 1 0 8 6 , 1 0 8 8 , 1 1 1 9| 3, |5| 7, 2, 103, 18 11 9, 8 ' 1 3 5 ] l |, 3 5 2 , | 2 2 | , | 2 g 0 , | 2 g | , t 2 s 2 , 1 2 9 4 |, 2 g 5 , 1 2 9 8 , | 4 7 . 71, 5 2 8 , 1 5 2 91,5 3 4 , 1 3 9 6 .1 4 1 5 , | 4 | 6 , | 4 | 9 , | 4 2 0 , | 4 4 0 ,| 4 6 , '7 1541 , 1 5 4 2 ,1 5 6 2 1

ti

266

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

T57. (JnivalenceOver Regionsother than the Unit Disc. [24, 25, 50, 55, 65, 120,326, 382,390,477, 597,760,986,1284, 1379,t42ll T58. Distortion Theoremsfor Meromorphic Functions of Topic 9. u l , r 3 4 , 4 9 0 ,5 3 5 , 5 9 5 , 7 0 8 , 9 3 4 , 9 3 5 ,9 3 9 , 9 4 0 , 9 5 0 ,9 5 1 , 9 5 2 , , 5 1 9 ,1 5 4 6 , , 4 7 5 ,1 4 7 6 1 , 1 5 8 ,1 2 4 3 ,1 4 1 9 ,1 4 3 6 1 1 1 1 2 1, 11 3 , 1 1 5 5 1

ts47l T59. Related Resultsfrom Analytic Funuion Theorv. [This topic is noi:being used.] T60. Multiply-ConnectedRegions. [ 5 6 , 8 8 , 1 2 1 , 3 2 8 , 3 7 9 , 3 8 39, ' 1 5 ,1 1 4 6 ,1 4 3 1 ,1 4 3 3 ] T6l. Distortion Theoremsfor Bounded Functions of Topic 22. 132,91, 213,236,265,295,297,308,351,3E8,418, 431,432,433, 854,883,891,895,904,1037,1050,1052.1078, 434,453,496,8C6, 1163,1165, 1229,1233,1262,1290,1298,1357,1381,i516, 15281 T62. Boundary Behavior (rate of growth of coefficientsor of functionals). 1 2 6 , 6 6 , 7 4 1, 2 6 ,1 2 9 ,1 5 l , 1 6 2 ,1 8 l , 1 8 9 , 2 1 0 , 2 r 2 , 2 2 1 , 2 3 4 , 2 7 9 , 3 ,5 2 , 3 5 4 , 3 6 13,6 5 ,3 6 7, 3 6 8 , 3 6 9 , 3 9 03, 9 1 ,4 1 5 , 287,332,349,351 4 1 6 , 5 3 85, 5 3 ,5 6 2 , 5 6 6 , 5 6 7 , 5 8 15,8 2 , 5 8 75, 8 8 ,5 9 0 ,5 9 6 ,5 9 8 ,6 2 0 , 6 3 8 ,7 0 5 ,7 9 7 , 8 0 28, 0 5 ,8 5 7 ,8 6 1 ,8 6 3 ,8 / 0 , E 7 1 , 8 7 2 , 8 7 4 . 8 7 6 , 8 9 8 ' 899, 900, 902, 925, 947, 956, 958, 960, 1027, 1029,1037, 1038, 1039,1043, 1046,1085,1099,1102,1124,ll6y',1167,1253,1322, 1434,1437,11i3, 1474,i475, 1476,i506, 15301 T63, Distortion Theoremsfor Starlike Functions cf lopic 6. [30, I 26, 13l, 163,191,I 92, 194,230,253,269,347, 377,388, 458, 4 5 9 ,5 2 4 ,5 4 3 , 5 8 76, 1 6 , 6 1 9&, 3 , 6 5 8 , 7 7 5 , 7 7 6 8, 0 2 , 8 5 78, 5 8 ,8 8 8 ' 9 1 2 ,1 0 0 9 .i c 8 - ? ,i c 8 5 , l i z z . 1 2 4 8 ,1 2 5 0 ,1 2 9 7 , 1 3 0 i .1 3 1 9 ,1 3 2 3 , 1335,1348, 1349,1350,1386,1387, 1416,1419,1474,1475,1500, l 5 l l , 1 5 2 7 , 1 5 3 3 , 1 5 3 71,5 4 3 ,1 5 5 8 1 T&. Di,stortion Theoremsfor Convex Functions of Topic 10. 619' [30, 139, 143,14, 145,147,194.247,252,266,388,479,543,

r

s

TOPIC REFERENCES

261

1250, 7 g 5 , 8 9 1 , 9 0 5 , 9 0 g6 |, 2 , 1 0 5 9 ,1 0 8 5 l, l 1 g , | | 2 0 , | | 2 2 , | 2 4 8 , 1 3 1 9 ,1 3 2 1 , 1 3 2 31, 3 3 5 ,1 3 5 3 ,1 3 8 2 ,1 4 9 1 1 Topic 14' T65. Distorticn Theoremsfor p-valent Functions o-i [ 8 C 3 ,8 0 7 , I 3 7 3 ] of Top;g 13' T66. Distortion Theoremsfor Typicatty-RealFunctions [ i 7 8 , 8 2 0 , 1 c o 5 ,l l l E , 1 2 0 i , 1 5 4 ( ) ] of Topic +5' T67. Distortion Theoremsfor Odd Univalent Functions 1252,368,458, 5241 - z+ S: T68. Distortion Theoremsfor Functions of the Clqss fQ) ezzz+ . . . Analytic and Univalentin lzl 266,2ll, 321,336' 338' 339', 147,74, 109, t34. 212,,222,241, 265, 5 3 5 '5 5 4 ' , 3 7 g , 3 8 33, 9 6 , 4 3 7 , 4 5 84, g 0 ,4 g 3 ,5 2 5 ,5 2 8 ,5 2 9 , 5 3 15' 3 3 ' 8 6 4 ,9 0 5 ,9 | 4 , , 5 7 9 , 5 9 56, 1 3 , 6 2 2 , 6 3 0 6, 7 | , 7 2 4 , 7 3 87, 4 | , 8 2 9 . 8 4 6 , 1 2 0 0 ,| 2 | 3 , 9 5 1 , ) ( , 9 , 1 0 5 0 ,| 0 7 7 , 1 1 1 0 ,1 1 1 9 ,1 1 5 5 ,1 1 5 9 ,1 1 6 3 , 15011 1 2 1 8, 1 2 1 3 , 1 2 4 8 ,1 2 6 7 , 1 2 8 21, ,3 2 2 ,1 4 3 6 ,1 4 3 7 , 1 4 3 9 , 1 4 9 3 ' and T69. u-Convex, ..-Starlike Functions (Mocanu functions) Generalizations. 3 1 8 '3 5 3 '3, 5 5 ' [ 3 3 , 3 5, 9 5 , 9 7 , 9 8 ,l N , 1 0 5 , 2 3 9 , 2 8 9 , 2 9 0 , 2 9 1 , 2 9 3 ' g0 0 ,g ,g 3 5 ,9 5 8 ,9 5 9 , 9 6 1 , 9 6 6 , 9 6 7 , 9 6986' 9 ' 3 5 g ,7 7 7 , 7 i 7 8 , " 1 7 g , 7 g gg7,ggg,ggg,1000,1001, 1002,l00l , 1197,1195,1337' gg0, 996;,, 1342,l4l'7, 14181 T70. Bazitevii Functiores(and generalizations). 6 9 4 , 7 7 9 , 7 8 08' 0 8 '8 4 7' 9 3 1 ' 12,216,2lg,28g,2g0,2g3,353 65 , 8, 1055,1178, 956, 969, gg7, 1003,1004, 1006,1040, 1051,1054, 1 4 4 6 '1 5 1 2 1 l l 7 g , 1 l 8 l , l l g 4 , 1 2 4 6 ,1 3 2 4 , 1 3 5,5l M 3 , l M , T7 | . Functionso-fBoundedBoundary Rotation. g, 288,292,293' 340' 494'7M' ll7, 78, 172, 173, 177, 17 214,286, 965'970' 7 0 6 , 7 0 7 , 7 7 4 , 8 0 2 ,8 0 4 , 8 0 5 , 8 0 9 , 8 6 i , 8 7 5 ' 8 8 2 ' 9 6 0 ' 1 0 5 5 ,1 0 9 0 , 1 0 1 4 ,1 0 3 5 ,1 0 3 6 ,1 0 3 8 ,1 0 3 9 ,1 0 4 0 ,1 0 4 1 ,l M 3 , | 0 4 7 , 1274, 1113 , L l z l , 1 1 2 4 , 1 1 2 5 l,l 9 5 , 1 2 1 4 , 1 2 1 5 , 1 2 2 3 , 1 2 2 5 , 1 2 7 3 ' 1 3 4 1 ,1 3 4 3 ,1 3 4 5 ,1 3 8 8 ,! M 5 , 1 4 6 5 ,l 4 7 l l

26E

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

T72. Distortion Theorems Involving Coefficients (various classesof functions). I 3 2 , 9 1 ,3 8 8 ,M , 4 4 8 , 4 4 9 , 8 4 6 , 8 8 3 ,8 8 4 ,8 8 7 ,1 0 8 5 ,1 2 5 8 , 1 3 5 7 ,

r4371 (of various classesof functions). T73. Rodiusof Close-to-Convexity l9l, 142,214,221,222, 292, 340, 453,460,699,7 46,776, 802, 855, 858, 1033. 1076,1084,1124,1227,1352,1353,15431 T74. Distortion Theoremsof Close-to-ConvexFunctions of Topic 5. [194, 252, 440, 442,M3, 446,838, 912, 1085,1149,1178,1249, 12ffi, 1323,1327,1333,1340,15021 T75. Coefficient Bounds (relations)Jor Close-to-ConvexFunctions of Topic 5. t 1 1 3, M 0 , M 3 , 4 4 6 ,4 5 6 ,5 2 4 ,5 4 6 , 5 4 8 ,5 8 8 , 6 9 3 , 8 6 7 , 9 1 2 ,1 1 4 9 , 1219,1327,1333,1340,15021 T75. Distortion Theo,'emsfor Functions of Bcunded Boundc,ryRotatiort of Topic 7l. 1 1 7 2 , 2 8 32, 9 3 , 3 4 0 ,7 0 7 , 8 0 2 , 8 0 5 1, 0 1 4 ,1 0 3 5 ,1 0 3 8 ,1 1 2 5 , 1 2 2 3 , 1273,1343,14451 T77. Coefficient Bounrlsfor Functions of Bounded Boundary Rotation of Topic 7l. Ir72, 173, 177,286,288,340, 706,774,802,804,805,875, l0l4' 1035,1036,1038,1047,1090,1125.1223,1273,1274,1345,14/5,

r47ri T78. Distortion Theoremsfor Functions Convex in One Directicn of Topic 41. 1524,57l, 572, 1235,l30l l T7g. Coefficient Bounds for Functions Convex in One Direction of Topic 41. , 2 2 3 ,l 3 0 l l t l L 3 , 5 2 4 , 5 7 1 , 5 7 2 , 6 2 8 , 9 7 21, 2 1 9 ,1 2 2 C 1 T80. Distortion Theoremsfor Bazilevic Functions of Topic 70.

,J

TOPIC REFERENCES

269

[847, 1006,1051] BazilevicFuncticns of ropic 70' tgr. Coefficient Rounds(rerations)for 1446] [358, 694,956,1006,|M:J, cf {JnivqlerfiFunctions' Tg2. Linear ccmbinations, Products, 1 3 2 . , 3 6 , 9 1 , 1 4 2 , 2 0 5 , 2 1 ! , 2 1 4 , 2 4 8 , 2 6 9 ' 3 58 1'440',446',451',460', 8 5 5 ' , 5 9 ' i,0 1 8 ' ,1 0 3 3 ' , 4 6 8 , 4 7 5 , 4 7.7 5 2 6 ,5 5 ? , , 6 7 8 , 7 1 5 , 7 g 5 , 8 3 ? ' 1355 , \ 3 5 7 ,1 3 6 1 ,1 3 9 6 , 1 0 8 9 ,l 1 0 9 ,| 2 2 7 , | 2 4 1 , | 2 6 4 , | 3 3 4 , 1 3 3 8 , 1400,1469,1526,1536,1542,15481 'Topic (a-starlike) Functions of a-convex Theorems for Distortion Tg3. 69. 1,342,I 5481 1291,293,777, 958, a-CotNex (a-stariike)Functions Tg4. coefficient Bounds (rerations)for of ToPic 69. 1291,358,777,778,77g,780,966,1417'1418'15481 T85. Univalenceof Integrals' 134,71,72,g1,94,95,gg,102,105'139'147',142',203'205'214' 2 2 4 , 2 2 8 , 2 4 8 , 2 5 g , 3 5 7 , ' 5 2 7 , 6 9 7 ' 6 9 8 ' 7 4 6 ' , 8 2 8 ' , 9 0 61' ,395235' ,' , 9 2 8 ' , l 2 3 l ' 1 2 9 7 '1 3 0 1 ' , 1 0 5 0 ,1 0 5 2 ,1 0 5 3 ,I I I 1 , I I 2 4 , l l g g ' 1 2 2 7 ' 1 3 5 5 ,1 5 4 1 , 1 5 M , 1 5 4 8 ,l 5 6 l l (and related classes) Tg6. Distortion Theoremsfor Bieberback-Eilenberg Functions of ToPic 34' 646,651] [ 9 , I 1 , 1 5 , 1 3 8 ,5 0 9 ,5 1 1 , Bieberbach-Eilenberg(ond Tg7. coefficient Bounds (relotions) for Functions of Topic 34' related classes) , 1 1 , 5 1 2 , 6 0 8 1, o 2 U [ 1l , 1 5 ,5 O 9 5 T88. ExtremePoint TheorY' [182,186,187,188,18g,2'73,284'387'500',541',542',s4y'.',545', 546,547,548,550,551,574,575,576'577'578',585',709',807',912' 9 1 3 ,9 1 6 ,g 4 2 , 1 2 4 9 , 1 3 3 51,3 3 6 '1 3 4 0 1

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

210

T89. Functions of Bounded Index' [40] , 402, 403, 699, I 187] T90. Entire Functions.

1192,1243,1302,1304,1306,

[400, 404, 406, 5'19,699,817' 1029, , 3 1 0 ,1 3 1 l ' 1 3 1 21, 3 1 51, 3 1 61, 3 1 7 1 13071 , 3 0 8 ,1 3 0 9 1

TABLE 1 which Following is a list of those referencesin this bibliography in included rrot were were publishedPrior to the Year 1966and which BibliographYI. Year

References

1950 1955 1959 I 960

u 4841 u 4851 12551 u059,1060,

r95l 1962 1963 t964

i965

[ 3 4 17, 8 1 ,1 3 2 81, 3 6 61, 5 1 6 1 1782,982,14861 , t{3 ,877,1378J u 4 9 , 1 5 0 , 3 7 2 , 6 2 i6, 4 5 7 758,782,784,785, [ 3 7 ,81 , 2 3 4 , 3 0 03, 1 2 , 4 9 86, 7 0 , 7 3 1 , 7 4 1 , 9 8 3 ,r l l 7 , 1 1 6 91, 2 0 8 1 , 52,759.786,'187, 07 , 67 u , 3 8, 4 5 , 1 4 8 , 2 3 53,1 0 ,3 7 3 , 4 1 4 , 6 5 6 1212,1256, , g o s ,8 7 8 ,9 4 7 , 9 8 49. 8 5 ,1 0 1 1 1, 0 6 1 , 1 1 4 6ll';3, 1257,1380,1427,1436,15461 2',76,31l,330, 374,375', 14,39, 42, 51,58, 66, 127, l-28,236, 68i' 4 1 7 , 4 2 4 , 4 3 6 , 4 6 5 , 4 g g , 55 01 03 , ,5 1 6 ,6 1 5 ,6 3 6 , 6 4 6 , 6 7' 7 837' 684, 716,736,7 53,7 55,788,790,825,826,827,828, 836' 9'.19' 842,843,851,866, 867,87g,903,972,975, 976,977,978' ll3i', i l05, 980,986, 1034,1064,1076,1077,1078,1093,1094, l23l' I l - ? 8 ,I 1 4 9 , 1 1 5 0 ,I l 5 i , 1 1 7 4 ,l l 3 2 ' 1 l 9 E, i 2 0 9 , l 2 l 9 ' L42l' 1419, 1264,lz]t, t2l2:, izig,l28l, 1365,1381, 1392, |487, | 4 2 8 , | 4 2 q 1 4 3 0 ,| 4 4 7 , | 4 4 8 , t + l g , 1 4 5 0 ,l 4 5 l , | 4 5 2 , , 5 5 1 ,t 5 5 2 . 1 5 5 3 1 1 4 8 8 ,1 5 5 0 1

A

TOPIC REFEP.ENCES

211

TABLE 2 which Following is a list of those referencesin this bibliography publishedduring the year 1975' $,/ere 3 5 7 , 3 g 7 , 5 4 85, 4 9 , 5 5 05, 7 8 ,5 8 0 ' 5 9 4 ' u 1 6 , 1 5 3, 2 1 6 , 2 ' t 8 , 2 7 2 , 2 g 0 , 3 3 3 , 10|.',1 ! 50' 9 9 ' 6 5 2 , 6 8 05, 9 1 , 7 0 8 , 7 3 g , 8 2 2 , 8 4 9 ,8 i 4 , 9 1 6 , 9 4 3 , 9 6 4 , 9 6 5 ' , 3 4 0 ,1 3 4 3 ,1 4 1 0 ,1 4 3 9 ,i 5 4 4 ) 1 1 8 4 ,1 2 6 2 ,i 3 0 5 , t 3 3 € . 1

TABLE 3 this Following is a listing of the total number of researchPaPersin bibliographywhich were publishedin eachof the given Years. Year

Total Number of PdPers

1966 lvo/ 1968 r969

r23

r970 197|

r972 r973 t9'14 t975

110 107 130 t46 t49 160 166 IM t25

272

B IBL IOGR AP H YOF SC H LIC H T FU N C TION S

TABLE 4 Followingis a list of Math. Review(MR) numbers(which had not in beenavailableat time of first publication)for someof the References the Bibliography,Part II. Ref. 17

MR# Ref. MR54 #2939 186

MR# Ref. MR53 #5849 332

MR# Ref. MR52 #8407 519

MR53 #5845

MR#

23

53 3297

194

53 788

345

52 11029 547

53 I1036

36

53 3288

20s

57 9950

3s9

53 3286

548

53 11036

37

54 528

222

54 7768

360

56 r2250

594

53 792

53 801

234

52 I l03l

366

52 t4259

632

54 2946

'/6

tt?

79

53 5848

258

3314

367

52 l 1030 678

52 1426r

87

54 5456

264

54 545I

370

57 t2837

52 t427|

153

54 525

271

53 8427

400

52 l 1039 720

57 r2839

r66

52 r42s8

303

53 l iu31

451

57 3372

54 54s7

175

54 537

320

52 ! l02r

496

53 I1043 776

780

52 14266 965

52 t1024

52 1262 it027

53 1376 5844

803

53 l1038 l0l8

52 53 t4263 1270 8409

52 r4265

805

52 53 r4268 1022 5846

822

52 t4267 1043

835

53 3282

54 2943

52 1090 rr025

707

758

t377

53 l1037

53 58 1280 22527 1388 3290 l3t8

54 5465

55 1425 r0662

1326

54 5479

53 1465 13549

TOPIC REFERENCES

MR# Ref. MR# Ref. 58 52 849 t4262 I 1 6 6 I 1 0 1 i 3.36 52 54 1358 11026 1 181 859 13057 53 53 1362 5847 I 1 8 3 862 I 1040 52 55 1 1032 1363 1 2 0 8 653 896 56 54 137| s862 554 1250 963

Ref.

MR# 54 294J

Ref.

MR#

53 1433 8 4 1 0 53 53 8429 1530 11041 52 r42& 53 8408

153I

54 2948

r532

53 3287

56 5857

Corrections

Reference 385 607 618 692

sameas

Reference 384 604

6r7 126

is Todorov' Pavel Notes (a) Reference1094: author Pletneva'T . G . (b) Ezroh;, T. G. is sameauthor as

LIJ

274

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

BIBLIOGRAPHYOF SCHLICHT FUNCTIONS 1) Part III (1976-198

CONTENTS Preface Bibliography Prior to Year 1976 Table l. References in Year lg82 2. References Table Table 3. Number of ReferencesPublisher!Each Ycar Corrections.

. 275 276 351 352 .,*352 353 .,i.

;,

J{

-

PREFACE

215

PREI.-ACE

tc contains1025references Dib'ography of SchlichtFunctions,Part III, (Schlicht)and multivalent publicationsin the theory of analyticunivalent through r981 and is a continuafunctions.part III coversthe ),ears19'76 Parts I' II' describedin tion of Bibliography of Schiicht Functions, earlierpages. and which werenot inSomePapersPublishedPrior to the year 1976 I. Somepaperspublishedir cludedin Parts I, II are now listedin Table numbers(MR) are inthe vear 1982are listedin Table II' Math. Review cluded for most references' Abstractshavebeen Part III differs from Parts I,II in two respects' and cross-indexlistingsare omitted and also no subtopic crassification justified becauseof their included. The omission of abstractsis easily results in the theory of transient value. classification of the various are usedin Part I' 90 subSchlichtfunctionsinto subtopics(68 subtopics and betweenreferences topics are usedin part II) and cross-indexlistings of hundreds task requiring subtopicsis a very valuablebut monumental prior to the publication hours of work-precious time not available deadlinefor Part III. S. D. Bernardi July 1982

t

216

BIBLIOCRAPHY OF SCHLICHT FUNCTIONS

BIBLIOGRAPHYOF SCHLICHT FUNCTIONS (Part III) Sect' III 1. Abe, H. On some analyticfunctions. Mem. Ehime univ.

7 (t97|t,tro.4,tff-IQI: MRK lzk77. Engrg.

2. Abe. H. On multivalentfunctions in multiply connecteddomains.l. Proc. JapanAcad. 53 (1977),no. 3, 116-ll9; MR 56 #594. 3. Abe, H. On multivalent functions in multiply connecteddomains' lI. Proc.JapanAcad. Ser.A lvIath.Sci.53 (1977),no.2,68-71;MR 58 #6210. 4. Abiarr, A. The coefficients cf the Laurent expansion of analytic -functions.Arch. Math. (tsrno) 13 (1971),no. 2, 65-68' 5. Abian, A. Hurwitz' theorem implies Rouch€'s theorem. J' Math' A n a l . A p p l . 6 l ( 1 9 7 7 )n, o . 1 , 1 1 3 - 1 1 5 . 6. Abian, A.; Johnstotr,E. H. Zeros of partial sums of the Laurent l' seriesof anatyticfunctions. KyungpookMath. J. 2l (1981),no' 87-90. 7 . Abu-Muhanna, Y.; MacGregot, T. H. Variabitity regions for by bounded analytic functions wi;th apptications to families defined

FUNCTIONS (PAI(T iII) BIBLIOGRAPHY OF SCHLTCHT

271

subordination.Proc.Amer.MathSoc.s0(1980),22-l-213;MR 8 1m:30022. points of families of g. Abu-Muhanna, y.; MacGregor,T. H . Extreme 176 to cont'ex mappings' Math' Z' analyticfunctions subord;nate ; R 82d:3C02i' ( I 9 8 1 ) ,n o . 4 , 5 1 1 - 5 1 9 M T. H. Families of real and SymMacGregor. g. Abu.Muhanna, Y.; no' Amer' Math' Soc' 263(1981)' metricanolytic functions.Trans. l , 5 g - 7 4 ;M R 8 2 a : 3 0 0 1 1 ' mapping' inequalityinvoh'ingconformal lc. Acker, A. An isoperimetric g77)' no' 2' 730-234;NIR 57#3364' (1 Proc. Amer. Math. Soc' 65 Nores, in un'ivarent functiorts. Lecture ,,. AharonoV,D. speciar toiiri ' UniversitYof MarYland(l 971) A minimal-qreaproblem in conforS' lZ. AharonoV, D.; Shapiro, H' of the Symposium on complex mal mapping. (Abstracti-eroc. _ 1973,pp. i-5' London Math' canterbury, Kent, uni". Analysis Soc.LectureNoteSer.No.|2,CambridgeUniv.Press,London (]j7$; MR s4 #526' A short proof of the Denioy coniecture' 13. AharonoV,D.; Srebro,v. B u l l e t i n ( N . S . ) A m e r . N i a t n . S o c . 4 , n o . 3 ( M a y 1 9a3 8 1 ) . aq of a betweenthe coefficients and 14. Ahlfors, I- V. An inequality (1976). Soc. Transl. (2) vol. 104 univalentfunctiot,. Amer. Math.

pf;r:l;ltt. r5.

of fyn:t:::: ':i'!,"!l^'n,the unit disc' certainctasses

5 (1971)'Do' Z' 3'79-389' Bull. Inst. Math' Acad' Sinila tvith on stsrtike and convexfunctions K. P. Jain, ?.; o. Ahuja, 16. (2) 3 Bull' MalaysianMath' Soc' missingand negativecoefficienfs' ( 1 9 8 0 ) ,n t . 2 , 9 5 - 1 0 1 ;M R 8 2 d : 3 0 0 1 3 ' value solvabitityof inverseboundary l7 . Aksent'eV,L. A. The u-nivale'tt 4)' (1 Kraev' zadacam vyp' I I 97 problems. (Russian)Trudy sem. 9 - 1 8 ;M R 5 7 # 6 5 2 '

1 8 . A k s e n t , e V , L . A . ( ] n i v q l e n t c h a n g e o f g76),30-39; p o r y g o n a l rMR J.om ins.(Russian) 58a#22522' 13il zadacamvvp. Kraev. Sem. Trudy 1 9 . A k s e n t , e v , L . A . ; G a i d u k , V . N . ; M i k kproblem a , V . P . T h eau regular n i v o l efunc' nt for value boundary inverse the of solvability (Russian)Trudy Sem' Kraev' tion in a doubly connectedregion ' -8; MR 56 #15948 ZaaacamVvp' 12 (lg7 5)' 3 z 0 . A k s e n t , e v , L . A . : K u d r j a s o v , s . N . S o m e c o n dvarue i t i o nproblem s f o r t h efor inverseboundary univarenceof the sorution'ofan Vyp' 6 f1$V Sem' Krle-v' Zadacam a symmetricprofite' tnt"iunl (1969),3_15.Foru,.ui.*olthisitemseeZbl236#76007;MR58

# r 7l r 3 .

zIEBIBLIOGRAPHYoFSCHLICHTFUNCTIONS

of some 21. Al-Amiri, H . s. Applications of the domsin of variability (Polish and functionals within the classof Caratheocloryfunctions. Sect.A Russiansummaries)Ann. univ. Mariae curie-Sklodowska ; R 81e:30019' 3 l ( l 9 7 7 ) , 5 - 1 4( 1 9 7 9 )M Rev' 22. Al-Amiri, H. S. Certain anulcgy of the a-convexfunctions' MR 80i: RoumaineMath. PuresAppl.23 (1978),no. 10,1449-1454; 30017. in the 23. Al-Amiri, H. S. Certain nth order dif-ferentialinequqlities MR complexplane. canad. Math. Bult. 2l (1978),no. 3 ,273-277; . 80m:30002 within the 24. Al_Amiri, H. s. The domain of variobitity of afunctional summary) classof univolent starlike fuitctions. (Scrbo-croatian 81e:30018' G l a s .M a t . s e r . I I I 1 4 ( 3 4 )( 1 9 7 9 )n, o . 1 , 5 5 - 6 6 ;M R prestsrlike functions' J' 25. Al-Amiri, H . S. Certain generqlizationsof MR Austral. Math. Soc. Ser. A 28 (1979), no. 3, 325-334; 81b:30018. Ann. Polon. Math' 38 clerivatives. 26. AI-Amiri, H. S. On Ruscheweyh ( 1 9 8 0 )n, o . 1 , 8 8 - 9 4 ;M R 8 2 c : 3 0 0 1 0 ' 27. Al-Amiri, H.; Mocanu, P. T. certain sufficient conditions for gnivslencyo,f the classc'. I. Math. Anal. Appl. 80 (1981),no' 2, 387-392;MR82g:30033. Proc' 28. Al-Amiri, H.; Mocanu, P. Spiratlikenonanalyticfunctions' 5 ;R 8 2 j : 3 0 0 2 8 . A m e r . M a t h . S o c . 8 2( 1 9 8 1 ) , 6 1 _ 6 M in the theory of continustions 29. Aleksandrov, I. A. Parametric (1976)' 343 pp' univalent futnctions. Izdat. "Nauka," Moscow 2 . 0 8 r ;M R 5 8 # 1 0 9 9 . equation' 30. Aleksandrov,I. A. A caseof integrction of the Lowner MR (Russian)sibirsk. Mat. z. 22 (1981),no. 2, 207'209, 238; 8 2 f: 3 0 0 1 7 . problemsfor svstems 31. Aleksandrov,I. A.; Andreev,v . A. Extremal Sibirsk. Mat' Z' 19 (Russian) of functions without common vqlues. ( 1 9 7 8 )n, o . 5 , 9 7 0 - 9 E 2 ,l 2 l 3 ; M R ' 8 0 d : 3 0 0 i 8 ' conJormollymap 32. Aleksandrov,I.A.; Cvetkov,B.G. Functionsthat no' I '4-25' the strip into itsel,/.(Russian)Sibirsk.Mat. Z.2l (1980), 235. properties-of 33. Aleksandrov, I. A.; Mandik, v. P. Extremal 7" 2 simultoneouslyp-valent fuiictions. (Russian) Sit irsk. Mat' (1981),no. 4, 3-13,229;MR E2i:J0028' A.optimal t:!' 34. Aleksandrov,I. A.; Zavozin,G. G.; Kopanev,s. (Russial) Dif' trclsin coefficientproblernsfor univoteit ,frmcticns. 771; MR 54 ferencial'nyeUravnenijal? (1976),no. 4, 599-611, #536.

(PART III) BTBLIOGRAPHYOF SCHLtcHT FUNCTIONS

219

generalizedareas in the case oJ 35. alenicyn, J. E. Inequaiities for with circular cuts' multivalent conforrnal ,ropping't of domains (Russian)Mat.Zametkizg(19E1),no.3,387-395,479;MR . 629:3C040 o-fa form o-fa multiply connected 36. Alenicyn, J. E . On the !eastareL (Russian)Mat' of p-sheetedcoriformal mappings' dontqin in cr clas.s ' Zametki30 (1981),no' 6, 807-812'95'1 problems Brarrnan'D. A. Research 37. Andersofl,J. lr4.;Baith, K. F.; Math' Scc' 9 (19'77)'llo' 2' in camplex anal.vsis.Buli. London 1 2 9 - 1 6 2M ; R 55#12899' Hypernorma! meromorphicfunc' 3g. Arrderson,J. M.; Rubel. L. A. no' 3, 301-309;MR 80b:30026' tions.HoustonJ. Math. 4 (1978), L' Coefficient multipliers of Bloch 39. Anderson, J. M.; Shields,A' f u n c t i o n ^ s . T r a n s . A m e r . M a t h S o c . 2q2certain 4 ( | 9 7 6crdss ) , n oof . 2functions ,255.265. 40. Andreev, \,. A. Extremistprobiems for disc. (Russian)Dokl' Akad' that are regular snd bctriaed in the N a u k S S S R z z s ( 1 g 7 6 ) , n o ' 4 ' 7 6 9 - 7 7 1 ; M R 5 4 # 1domains' 3 0 6 7 ' (Ruso,fnonovertapping problems certain A. v. Andreev, 41. 715;MR 55 #3235' 3 sian)Siblrsk.Mat. Z. i (1976),no. ,183-498' ond convexity of certain 42. Anh, v. v.; Tuan, P D'. on starlike:ness analyticfunctio;ts.PacificJ.Math.69(1977),no.1,1_9,MR55 #5848. p-converity of certainstsrlike univalent 43. Anh, V. V.; Tuan, P' D ' On 10' Matlr. Pures APPI' 24 (1979)'no' functions. Rev' Roumatne 1 4 1 3 -1 4 2 4 M R 8 1 b : 3 0 0 1 9 ' An extremalProblemfor univalent 44. Astahov,V. N. (Astahov'V' M') Nauk Ukrain' SSR Inst' analYtic Junctions' (Russian) Akad. Processov(1977),18-24; Kibernet.PrePrintNo' 11 Teor' Optimal.

I\{R 58 #28472. 4 5 . A s t a h o v , V . M . T h e r a n g e o f v a l u e s o . f a s y ssummary) t e m o f f u nDokl' ctionalsin (Russian,English univalent funirfoir. of c/asses MR 58 no. 3, 195-t98,284; Akad.Naukukrain.ssR Ser.A (1978), #1129 ., ' - ^t -.-i,,ntnnt on the crassof univarenr 46. Astahov, v. M . The rangeof a functionar (Rrrssian)Theory of functions and functions with rent coefiicrerrc." mappings(Russian),"NaukovaDumka"'Kiev(1979)'pp'3-27' t 74 ; I V I R8 1 d : 3 0 0 1' 3 Gutljans'kli,V..J. Someextremal 47.Astahov,V. N. (Astalrov,V.M.); (Russian)Metric quesproblems for univalent analyticfunctions' mappings(Russian)"'Naukova tions of the theory of functionsand MR 58 #28475' Dumka," Kiev (1977),pp' 3-19' 166; of on some classes 48. Atzmon, A. Extremallinrtions for functionals

2E0BIBLIOGRAPHYoFSCHLICHTFUNCTIONS

(1978),no' 2, 333-338; analyticfunctions. J. Math. Anal. Appl. 65 MR 80c:30008. mappingand 49. Aumann, G. D,stortion of a segmentunder conformal International relatedproblems.Proceedingsof the C. Carath6odory Athens, Soc., Math. Symposium(Athens, |973), pp. 46_53.Greek 1974;MR 57 #&06. derivstivefor the 50. Avhadiev, F. G. Application of the schwarzian value probstudy of the univalent solvsbitity of inverse boundary 7 (1970),78-80; lems. (Russian)Trudy Sem. Kraev. zadacamvyp. MR 58 #17lt7. the half-plane' (Rus51. Avhadiev, F . G. some univslent mappings of MR 57 #642' (1 sian)Trudy Sem.Kraev. zadacamvyp. l1 974),3-8; and BMO' Indiana 52. Axler, S.; Shields,A. Extremepoints in vMo U n i v . M a t h . J . 3 l ( i 9 8 2 ) ,D o ' 1 , 1 - 6 ' mean oscillation' 53. Baernstein, A., II. (Jnivalenceand bounded (1977);MR 56 #3281' MichiganMath. J.23 (1976),no. 3 ,217-223 *-function solvesextremalproblems' 54. Baernstein,A., ll. How the Mathematiciarts Proceedings of the International Congress of 1980; (Helsinki, 1978),pp. 639-644,Acad. Sci. Fennica,Helsinki, MR 8lb:30028. for coniugatefuncticns' A., II. Somesharp irrcqualities 55. Baerns*-ein, MR 80g:30022' Indianauniv. Math. J.27 (1978),no. 5, 833-852; coefficientsof func56. Baernstein,A., II.; Rochberg,R. lv[eansand Prcc' Cambridge tions which omit o sequenci of values. Nlath. -57' Philos. Soc. 81 (1977),no' I , 47 inversecoefficientsof 57. Baernstein,A., II.; Schober, G. Estimatesfor Math' 36 (1980)' from ir,tegralmeans.IsarelJ. univalentfunci:tions no. I ,75-82; MR 82a:30022' (Russian)Akad 58. Bahtin, A. K . Coefficientsof univaientlunctions. (197E),8pp': MR Nauk Ukrain. ssR Inst. lvrat.Prepring-No.32 80c:30015. akaci' Nauk Ukrain' 59. Bahtin, A. K . Functi,ns cf classs. (Russian) Teorii Funkciii SSR Inst. Mat. Preprint(1979),no- 12, Issled'po Topologii,3-13; MR 81k:30014' of the coefficientsof 60. Bahtin, A. K. (Bahtin, o. K .) some properties and its ap' univslentfunctions. (Russian)The theory of functions Kiev (1979)i plications(Russian),pp. 3-8, 2U7,"NaukovaDumka"' MR

8lgz3lJ024'

n) - : - , , ^ ^ t c . . - n l i n n o o.f nr, s' (Russtat ",.? of functions n f c/ass 51. Bahtin, A. K. on coefficients Dokl.Akad.NaukSSSR254(1980),no.5,1033_35. (Rrrssian)Akad' 62. Bahtin, A. K. On functions of the cel'fer class.

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NaukUkrain.SSRInst.Mat.Preprint(1980),oo-.3l,oNekotor. Z a d a c a h v T e o r . o d n o l i s t . F u n k c i i , 3 - 1 0 ; M R 8 2 f : 3 0 0 2(Russian) 2. univalent functions' of coefficients of Extrems K. A. 53. Rahtin, Preprrnt(1980)'no' 30' 20 pp' Akad. Nauk ui
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7 7 . Bajpai, S. K. The coefficients of power seriesgiving a coefficients characterizationfortype. (Italian summary)Rend.Mat. (7) I (1981), no.2,293-303. 7 8 . Bajpai, S. K.; Dwivedi, S. P. On the radii of starlikeness,convexity and closeto convexityof p-valentfunctions. Rev. RoumaineMath. PuresAppl. 23 (1978),no. 6, 839-842;MR 58 #17065. 7 9 . Bajpai, S. K.; Dwivedi, S. P. Certain classesnf univalent anslytic functions. Rev. ColombianaMat. 13 (1979),no. 3, 2O7-243;MR 81i:30016. 80. Bajpai, S. K.; Dwivedi, S. P. Certain convexity theorems for univalent analyticfunctions. Publ. Ins+".Math. (Beograd)N. S.) 28(42)(1980),5-l l 8 1 . Bajpai, S. K.; Mehrok, T. J. S. On rqions of a-convexityfor subclassesof starlike functions. Indian J. Pure Appl.Math.5 (1914),no. 10,902-908;MR 55 #5849. 82. Baranowicz, Jozef, On the coefficients of bounded real univalent functions.Ann. Polon. Math.32 (1976),no.2, 135-144.@rrata insert);MR 54 #10589. 8 3 . Barnard, R. W. On quasr-starlike functions. Ann. Polon. Math. 32 ( 1 9 7 6 )n, o . 3 , 3 0 3 - 3 0 8M ; R 54 #529. 8 4 . Barnard, R. W. On bounded univalentfunctions whoserantes contain a fixed disk. Trans. Amer. Math. Soc. 225(,1977),123-144;MR 54#10585. 85. Barnard, R. W. ,4 generalizationof Study's theorem on convex maps. Froc. Amer. Marh. Soc. 72 (1978),no. 1, 127-134 MR 80k:30014. 8 6 . Barnard,R.W. On Robinson'sl/2 conjecture.Proc. Amer. Math. S o c .7 2 ( 1 9 7 8 )n, o . 1 , 1 3 5 - 1 3 9M ; P -8 0 j : 3 0 0 1 4 . Barnard, R. W.; 87. Kellogg, C . Applications of convolutio;t operotors to problems in univalent .function theory. Michigan Math. J. 27 ( 1 9 8 0 )n, o . l , 8 1 - 9 4 ;M R 8 l f : 3 0 0 0 6 . 8 8 . Barnard, R.; Lewis, J. L. Subordinationiheorems1or scnneclosscs of starlikefunctions. Paciiic J. Math. 56 (1975),no.2,333-366; MR 52 #721. 8 9 . Barnard, R.; Lewis, J. L. Correctionto: "Subordination theorems for .someclassesof stcrlikelunctions" (Facific J. Math. 56 (1975), nc. 2, 333-J66).Pacific J. Math. 6l (1975),no. 2, 607:'MR 53

#584r. 90. Barr, A.; Causey,W. M. The radius of univalcn:z o.f certain classes of analyticfu;tctions.Indian J. Math. 17 (1975),no. I ,33-39. 9 1 . Barsegfatr,G. A. Ceernetricsiructure of the image of the circle in

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of rotional functions with sintplepoles and politive residues classes to the ttncoveringof the structure of magneticfieldt o"fsystemsof equally directed direct currants. (Russian:French summary) Plov; R 58 ) ,o . 1 , 3 1 7 - 3 2 1( 1 9 7 7 ) M d i v . u n i v . N a u c n .T r u d . 1 3 ( 1 9 7 5 n #22529. 926. Todorov, p. G. On the unique maximal domain o"f univalenceo.f the derivative classo(v - lxR,) of the rational classo(R,). (RusDo. sian;Frenchsummary)Plovdiv. Univ. Naucn.Trud. 16(1978), 1 , 3 0 3 - 3 1 4( 1 9 8 0 ) . g27. Todorov, p. G. New expticit formulas for the coefficients of p-symmetricfunctions. Proc. Amer. Math. Soc. 77(1979)'no' l, 8 1 - 8 6 ;t v I R8 1 g : 3 0 0 2 1 . g28. Todorov, P. G. A simple proof of the Kirwan theorem for the radius of startikenessof the typicaily real functions and one new no. 4, 334-342; result.Acad. Roy. Belg.Bull. Cl. Sci. (5)66(1980), MR 82a:30021. g1g. Todorov, p . G. Radius of convexity for a l'{evanlinnu class of analytic functions. (Bulgarian; Russian and English summaries) ro. 1, 315-323(1980);MR Plovdiv.Univ. Naucn.Trud. 16(1978), 8 2 f: 3 0 0 1 3 . 930. Todorov. p. G. Limite de convexit| d'une classede Nevanlinnade no. 2, 127fonctions analytiques.Arch. Math. (Basel)34(1980), l2l;MR 8lk:30017. of 931. Todorov, p. G. New expticitformulas for the nth derivative I no. ,217-236. compositefunctions. Pacific J. Math.92(1981), g32. Todorov, P. G. Explicit formulas 1or the coefficients of Faber polynomials with respect to univalent functions of the clsss E ' P r o c .A m e r . M a t h . S o c .8 2 ( 1 9 8 1 )n,o . 3 , 4 3 1 - 4 3 8 ;M R 8 2 f : 3 0 0 1 6 ' cf 933. Todorov, P. G . Uniquenessof the maximal univalencedomain (Russian; the derivativeclassOi'-')(R,) of the rationcl classO(R"). I-itovsk. Mat. Sb. 21 (i981)' Lrthuanianand French summa,Iies) nc. I ,203-20u; MR 82j:t0024' g34. Townsend, D. w. Imaginary valuesof meromorphicfunctions m no' I ,225-242' the disk Pacific I. Math. 96(1981), Ctose-to-convex -functionsartd their 935. Trimble, S. Y.; Wright, D . J. 3' extremepointsin Hcrnich space.Monatsh.Math' 85(1978),no' 2 3 5 - Z M ;M R 5 8 # 1 1 3 5 5 . 936. Tsanov,v. v. (canov, v.v.) Extremepoints and uniformizati-o-n' c. R. Acad. Bulgaresci. 30(1g77),no. 2, l7g-t8l; MR 56 #5868' g37. Tsuji, H. A generalizationof Schwarz lemma. Math' Ann ' 75(' ( 1 9 8 1 )n, o . 3 , 3 8 7 - 3 9 0 .

i4

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345

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319

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,ilM

OF S C H LIC H T FU N C TION S(P A R T III) B T BL T OGR A P H Y

35r

RSR Ser' A (1975)' summaries)DopovicliAkad. Nauk Ukrain' ' n o . I 1 , 9 7 6 - 9 7 8 ,1 0 5 0 ;M R 5 8 # 6 2 0 7 integraltransformsin certain v. R. 1020. Zmorovir, V. A.; i.{ikolaeva, Englishand Russian oi ,uiratent functions. (Ukrainian; classes Ukrain. RsR Ser. A (1975)' summaries)popovidi Akad. Nauk ' n o - I 1 , 9 7 6 - 9 7 8 ,1 0 5 0 ;I U R 5 8 # 6 2 0 7 Y. Integral transformationwith 1021. Zmorovid,v. A.; Nikolaeva, R . l o g a r i t h m i c k e r t r c I s i n s o | n e c l a s s e s o f u n i v a i e (Russian)' n t f u n c t i o pp' ns.(Rusanalysisand prcbabilitytheory sian)Ir4athema.tical 6 6 _ . t 0 , 2 | | , . N a r r k o v a D u m k a , ' ' K i e v ( r 9 7 8 ; M R 8 2a-convex d:30016. v. A' (Pohilevitl Y' o'l rc22. Zmorovi6, v. A.; Pohilevi6, uk'ain' Mat' z' 31(1979)'no' 4' ( (R.ussian) functionsfor cY c. 431-433, 478; MR 8 I e:30026' O. On a-almostconvexfunctions' 1023. Zmorovir,v. A.; Pohilevi6,v . ( R u s s i a n ) U k r a i n ' M a t ' Z ' 3 3 ( 1 9 8 1 ) ' n o ' 5 ' 6 7 0 - 6 7 3(Russian) '718' Bloch functions' problems for Some V. I. 1024.Zuravlev, MR56#15903. Dokl.Akad.NaukSSSR236(|97.7),no.l,2l_22 and reichmilller spaces.(Rusr025. zuravrev,r .ti. univarentfunc;ions sian)Dokl.Akad'IrlaukSSSR250(1980)'no'5'104'7-1050;MR 81b:30085. Table 1 in this Bibliography(Part III) Forowing is a lisr of thosereferences year lg76 anrl which werenot included which werepublishedprior to the (Part II)' in eitherBibliography(Part I) or Bibliography Year Reference 1 4 5 1 4 6 ' , 1 5 2 ' 1 8 1 '8, 3 '1, 8 4 '1 8 5 ' 1 9 ' 7 5 1 g , 6 9 , 8 88, 9 , 9 0 , 9 2 , 1 2 5 , 1 3 3 , ' 1 9 0 , 2 3 8 , 2 7 7 , 2 g 7 , 3 0 5 , 3 4 C 3 6 5 ' 4 2 0 ' , 4 2 5 ' , 4 5 7 ' ,722', 4 6 5 740', '502'510' 66'7 ', 687', 713', 594,598,606, 625"643,650' 666' g4g', 5',12, ', g25' ', 964' 96',7 953',95',7 783, 7g2,'7g4,801,8rl, 853, 908, 9 7l , g 7 2 , 9 7 8 ,1 0 0 1 ,1 0 1 9 ,1 0 2 0 ' 394',466',468' 215'247',364',380', lg'74 12, 17, 51, 67,81,I 66,20l,2ll' 4 ' 7 8 , , 5 0 3 , 5 0 9 , 5 3 1 , 5 3 4 , 5 8 7 , 6 0 4 ' 6 6 5 ' 6 7 1 ' , 6 8 9944', ' , 6 9948', 0',691',712', 911',923' 924', 765,?80, 803, 844, 867"884, 885' 905' 99't. lg-131,49,,218,276,,357,453,697,720'7gl'816',897',996'

352

BIB L IO GR AP H YO F S C H L I C H T FU N C TION S

1972 l97l 1970 1969 1968 1967 t966 1965 1963 1962 1960 1959 1955 1953 t952 1946 1934 1933 t932 l9z8

263, 405,575, 7 lg, ggI , 904, 970. l l , 2 1 4 , 2 3 4 , 2 6 2 , 3 5 2 ,4 7 1 ,6 5 2 , 7 3 E , 7 3 9g,l 4 . g l 5 . 50, 261, 545,g I 0. 20, 260,439. 494. 437. 347. 5 1 3 ,6 3 4 . 749. 470. 748. 640. 662. 661. 660. 500. rt4. 499. 379, 621. 244.

r9z0 903. t9t4 243. 1913 242.

Table 2 Followingis a list of thosereferences in this Bibliography(Part III) which werepublishedduring the year l9E2: Referenc'es: 52, 1 6 7 , 3 8 3 5, 4 9 , 5 5 16, 9 5 .

Table 3 Followingis a listing of the total number of researchpapersin this Bibliography(Part III) which werepubl:shedin eachof the givenyears.

;:j'.k

(P A R T III) B IBL IOGR A P H YOF S C H LIC H T FU | { C TION S

353

Year Total Number o-f PaPers r9j6 1977 1978 1979 1980 1981

r99 148 r32 r43 130 107

II contains38 references' Notes For the year 1g76,BibiiographyPart a iotal while Belrliographypart IiI contains199references,-for of 237 references'

Corrections (Part III) inFollowing is a list of referencesin this Bibliography dicatingduPlicationsof PaPers: Reference sanleas Reference 989 990 9 101 1020

h.*-