Problems concerning sharp coefficient functionals of bounded turning functions

Muhammmad Ghaffar Khan; Wali Khan Mashwani; Jong-Suk Ro; Bakhtiar Ahmad; Muhammmad Ghaffar Khan; Wali Khan Mashwani; Jong-Suk Ro; Bakhtiar Ahmad

doi:10.3934/math.20231402

AIMS Mathematics

2023, Volume 8, Issue 11: 27396-27413. doi: 10.3934/math.20231402

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Problems concerning sharp coefficient functionals of bounded turning functions

1.
Institute of Numerical Science Kohat University of Science and Technology, Kohat, Pakistan
2.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
3.
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
4.
Govt. Degree College Mardan, Mardan, Pakistan

Received: 02 August 2023 Revised: 01 September 2023 Accepted: 08 September 2023 Published: 27 September 2023
MSC : 05A30, 11B65, 30C45, 47B38

The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors. We aim to establish a new subfamily of holomorphic functions connected with the hyperbolic tangent function with bounded boundary rotation. We investigate the sharp estimate of the third Hankel determinant for this newly defined family of functions. Moreover, for the defined functions family, the Krushkal inequality, the first four initial sharp bounds of the logarithmic coefficients and the sharp second Hankel determinant of the logarithmic coefficients are given.
- holomorphic functions,
- Hankel determinant,
- subordination,
- hyperbolic function
Citation: Muhammmad Ghaffar Khan, Wali Khan Mashwani, Jong-Suk Ro, Bakhtiar Ahmad. Problems concerning sharp coefficient functionals of bounded turning functions[J]. AIMS Mathematics, 2023, 8(11): 27396-27413. doi: 10.3934/math.20231402

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Abstract

The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors. We aim to establish a new subfamily of holomorphic functions connected with the hyperbolic tangent function with bounded boundary rotation. We investigate the sharp estimate of the third Hankel determinant for this newly defined family of functions. Moreover, for the defined functions family, the Krushkal inequality, the first four initial sharp bounds of the logarithmic coefficients and the sharp second Hankel determinant of the logarithmic coefficients are given.

References

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