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A Proof of Hall's Conjecture on Starlike Mappings
Author(s) -
Balasubramanian R.,
Karunakaran V.,
Ponnusamy S.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.2.278
Subject(s) - conjecture , class (philosophy) , order (exchange) , combinatorics , mathematics , pure mathematics , physics , computer science , artificial intelligence , finance , economics
In this paper we show that| f ( r e 1 θ) |− 1∫ 0 r| f ′ ( u e 1 θ) |d u ⩽ r − 1 arcsin r , 0 < r < 1 where f lies in the class of starlike functions of order ½, that is, which are regular and univalent for | z | < 1 and such that Re z f ′ ( z )f ( z )> 1 2 f o r | z < 1 |