Hankel inequalities for bounded turning functions in the domain of cosine Hyperbolic function

Muhammmad Ghaffar Khan; Wali Khan Mashwani; Lei Shi; Serkan Araci; Bakhtiar Ahmad; Bilal Khan; Muhammmad Ghaffar Khan; Wali Khan Mashwani; Lei Shi; Serkan Araci; Bakhtiar Ahmad; Bilal Khan

doi:10.3934/math.20231121

AIMS Mathematics

2023, Volume 8, Issue 9: 21993-22008. doi: 10.3934/math.20231121

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Hankel inequalities for bounded turning functions in the domain of cosine Hyperbolic function

1.
Institute of Numerical Science Kohat university of Science and Technology, Kohat, Pakistan
2.
School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China
3.
Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, TR-27010 Gaziantep, Türkiye
4.
Govt. Degree College Mardan, Mardan Pakistan
5.
School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China

Received: 05 May 2023 Revised: 28 June 2023 Accepted: 02 July 2023 Published: 11 July 2023
MSC : 05A30, 30C45, 11B65, 47B38

In the present article, we define and investigate a new subfamily of holomorphic functions connected with the cosine hyperbolic function with bounded turning. Further some interesting results like sharp coefficients bounds, sharp Fekete-Szegö estimate, sharp $ 2^{nd} $ Hankel determinant and non-sharp $ 3^{rd} $ order Hankel determinant. Moreover, the same estimates have been investigated for 2-fold, 3-fold symmetric functions, the first four initial sharp bounds of logarithmic coefficient and sharp second Hankel determinant of logarithmic coefficients fort his defined function family.
- holomorphic functions,
- Hankel determinant,
- Subordination,
- Hyperbolic function
Citation: Muhammmad Ghaffar Khan, Wali Khan Mashwani, Lei Shi, Serkan Araci, Bakhtiar Ahmad, Bilal Khan. Hankel inequalities for bounded turning functions in the domain of cosine Hyperbolic function[J]. AIMS Mathematics, 2023, 8(9): 21993-22008. doi: 10.3934/math.20231121

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Abstract

In the present article, we define and investigate a new subfamily of holomorphic functions connected with the cosine hyperbolic function with bounded turning. Further some interesting results like sharp coefficients bounds, sharp Fekete-Szegö estimate, sharp $ 2^{nd} $ Hankel determinant and non-sharp $ 3^{rd} $ order Hankel determinant. Moreover, the same estimates have been investigated for 2-fold, 3-fold symmetric functions, the first four initial sharp bounds of logarithmic coefficient and sharp second Hankel determinant of logarithmic coefficients fort his defined function family.

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