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Research Article | Open Access

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

Muhammad Ghaffar Khan1, Nak Eun Cho2( ), Timilehin Gideon Shaba3, Bakhtiar Ahmad4, Wali Khan Mashwani1
Institute of Numerical Sciences, Kohat university of science and technology, Kohat, Pakistan
Department of Applied Mathematics, Pukyong National University Busan 48513, Korea
Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
Govt. Degree College Mardan, Mardan 23200, Pakistan
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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.

Keywords

analytic functionsmodified sigmoid functionsubordinationHankel determinant2-fold and 3-fold symmetric functionZalcman conjuctureKrushkal inequality
CLC number: 30C45, 30D30

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 3133-3149
DOI: 10.3934/math.2022173

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Cite this article:
Khan MG, Cho NE, Shaba TG, et al. Coefficient functionals for a class of bounded turning functions related to modified sigmoid function. AIMS Mathematics, 2022, 7(2): 3133-3149. https://doi.org/10.3934/math.2022173

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Received: 21 May 2021
Accepted: 21 November 2021
Published: 15 February 2022
©2022 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)