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

Zhen Peng; Muhammad Arif; Muhammad Abbas; Nak Eun Cho; Reem K. Alhefthi; Zhen Peng; Muhammad Arif; Muhammad Abbas; Nak Eun Cho; Reem K. Alhefthi

doi:10.3934/math.2024761

AIMS Mathematics

2024, Volume 9, Issue 6: 15761-15781. doi: 10.3934/math.2024761

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

1.
School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China
2.
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
3.
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
4.
Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 30 November 2023 Revised: 05 April 2024 Accepted: 08 April 2024 Published: 30 April 2024
MSC : 30C45, 30C50

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.
- Hankel determinant,
- bounded turning functions,
- cosine hyperbolic function,
- logarithmic coefficient problems
Citation: Zhen Peng, Muhammad Arif, Muhammad Abbas, Nak Eun Cho, Reem K. Alhefthi. Sharp coefficient problems of functions with bounded turning subordinated to the domain of cosine hyperbolic function[J]. AIMS Mathematics, 2024, 9(6): 15761-15781. doi: 10.3934/math.2024761

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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.

References

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