Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
On the Fourth Coefficient of the Inverse of a Starlike Function of Positive Order
Toshiyuki SUGAWALi-Mei WANG
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2021 Volume 27 Issue 1 Pages 93-106

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Abstract

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.

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