Coefficient functionals for a class of bounded turning functions related to modified sigmoid function

Muhammad Ghaffar Khan; Nak Eun Cho; Timilehin Gideon Shaba; Bakhtiar Ahmad; Wali Khan Mashwani; Muhammad Ghaffar Khan; Nak Eun Cho; Timilehin Gideon Shaba; Bakhtiar Ahmad; Wali Khan Mashwani

doi:10.3934/math.2022173

AIMS Mathematics

2022, Volume 7, Issue 2: 3133-3149. doi: 10.3934/math.2022173

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Coefficient functionals for a class of bounded turning functions related to modified sigmoid function

1.
Institute of Numerical Sciences, Kohat university of science and technology, Kohat, Pakistan
2.
Department of Applied Mathematics, Pukyong National University Busan 48513, Korea
3.
Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
4.
Govt. Degree College Mardan, Mardan 23200, Pakistan

Received: 21 May 2021 Accepted: 21 November 2021 Published: 24 November 2021
MSC : 30C45, 30D30

The main objective of the present article is to define the class of bounded turning functions associated with modified sigmoid function. Also we investigate and determine sharp results for the estimates of four initial coefficients, Fekete-Szegö functional, the second-order Hankel determinant, Zalcman conjucture and Krushkal inequality. Furthermore, we evaluate bounds of the third and fourth-order Hankel determinants for the class and for the 2-fold and 3-fold symmetric functions.
- analytic functions,
- modified sigmoid function,
- subordination,
- Hankel determinant,
- 2-fold and 3-fold symmetric function,
- Zalcman conjucture,
- Krushkal inequality
Citation: Muhammad Ghaffar Khan, Nak Eun Cho, Timilehin Gideon Shaba, Bakhtiar Ahmad, Wali Khan Mashwani. Coefficient functionals for a class of bounded turning functions related to modified sigmoid function[J]. AIMS Mathematics, 2022, 7(2): 3133-3149. doi: 10.3934/math.2022173

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Abstract

The main objective of the present article is to define the class of bounded turning functions associated with modified sigmoid function. Also we investigate and determine sharp results for the estimates of four initial coefficients, Fekete-Szegö functional, the second-order Hankel determinant, Zalcman conjucture and Krushkal inequality. Furthermore, we evaluate bounds of the third and fourth-order Hankel determinants for the class and for the 2-fold and 3-fold symmetric functions.

References

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