Article
Version 1
Preserved in Portico This version is not peer-reviewed
On the Fourth Coefficient of the Inverse of a Starlike Function of Positive Order
Version 1
: Received: 13 November 2020 / Approved: 16 November 2020 / Online: 16 November 2020 (15:08:35 CET)
How to cite: Sugawa, T.; Wang, L.-M. On the Fourth Coefficient of the Inverse of a Starlike Function of Positive Order. Preprints 2020, 2020110428. https://doi.org/10.20944/preprints202011.0428.v1 Sugawa, T.; Wang, L.-M. On the Fourth Coefficient of the Inverse of a Starlike Function of Positive Order. Preprints 2020, 2020110428. https://doi.org/10.20944/preprints202011.0428.v1
Abstract
We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. 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.
Keywords
starlike function of order $\alpha$; inverse function; coefficient estimates
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment