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Research Article | Open Access

Sharp coefficient problems of functions with bounded turning subordinated to the domain of cosine hyperbolic function

Zhen Peng1, Muhammad Arif2 ( ), Muhammad Abbas2, Nak Eun Cho3, Reem K. Alhefthi4
School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Abstract

In the current article, we consider a class of bounded turning functions associated with the cosine hyperbolic function and give some results containing coefficient functionals using the familiar Carathéodory functions. An improvement on the bound of the third-order Hankel determinant for functions in this class is provided. Furthermore, we obtain sharp estimates of the Fekete-Szegö, Krushkal, and Zalcman functionals with logarithmic coefficients as entries. All the findings are proved to be sharp.

Keywords

Hankel determinantbounded turning functionscosine hyperbolic functionlogarithmic coefficient problems
CLC number: 30C45, 30C50

References

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 15761-15781
DOI: 10.3934/math.2024761

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Cite this article:
Peng Z, Arif M, Abbas M, et al. Sharp coefficient problems of functions with bounded turning subordinated to the domain of cosine hyperbolic function. AIMS Mathematics, 2024, 9(6): 15761-15781. https://doi.org/10.3934/math.2024761

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Received: 30 November 2023
Revised: 05 April 2024
Accepted: 08 April 2024
Published: 30 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)