文章基本信息

标题：On the Fourth Coefficient of the Inverse of a Starlike Function of Positive Order
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作者：Toshiyuki SUGAWA ; Li-Mei WANG
期刊名称：Interdisciplinary Information Sciences
印刷版ISSN：1340-9050
电子版ISSN：1347-6157
出版年度：2021
卷号：27
期号：1
页码：93-106
DOI：10.4036/iis.2021.R.01
出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：We consider the inverse function z = g ( w ) of a (normalized) starlike function w = f ( z ) of order α on the unit disk of the complex plane with 0 < α < 1. Krzyż, Libera and Złotkiewicz obtained sharp estimates of the second and the third coefficients of g ( w ) in their paper (1979). Prokhorov and Szynal gave sharp estimates of the fourth coefficient of g ( w ) as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of g ( w ) together with explicit forms of the extremal functions.
关键词：starlike function of order α;inverse function;coefficient estimates