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The sharp bound of the third Hankel determinant for starlike functions

  • Bogumiła Kowalczyk ORCID logo , Adam Lecko ORCID logo EMAIL logo und Derek K. Thomas
Veröffentlicht/Copyright: 30. Juli 2022

Abstract

In this paper, we prove the sharp inequality | H 3 , 1 ( f ) | 4 / 9 for starlike functions 𝑓, where H 3 , 1 ( f ) is the third Hankel determinant, thus solving a long-standing problem.

MSC 2010: 30C45; 30C50

Acknowledgements

We sincerely thank the reviewer for constructive comments that helped to improve the clarity of this manuscript.

  1. Communicated by: Shigeharu Takayama

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Received: 2021-12-04
Revised: 2022-04-01
Published Online: 2022-07-30
Published in Print: 2022-09-01

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