The sharp bound of the third Hankel determinant for starlike functions-Reference-Cited by-同舟云学术

The sharp bound of the third Hankel determinant for starlike functions

Published:2022-07-30 Issue:0 Volume:0 Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Kowalczyk Bogumiła¹^ORCID,Lecko Adam¹^ORCID,Thomas Derek K.²

Affiliation:

1. Department of Complex Analysis , Faculty of Mathematics and Computer Science , University of Warmia and Mazury in Olsztyn , Olsztyn , Poland

2. Department of Mathematics , Swansea University Bay Campus , Swansea , SA1 8EN , United Kingdom

Abstract

Abstract In this paper, we prove the sharp inequality | H 3 , 1 ⁢ ( f ) | ≤ 4 / 9

\lvert H_{3,1}(f)\rvert\leq 4/9

for starlike functions 𝑓, where H 3 , 1 ⁢ ( f )

H_{3,1}(f)

is the third Hankel determinant, thus solving a long-standing problem.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2021-0308/pdf

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3. C. Carathéodory, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64 (1907), no. 1, 95–115.

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