Sufficiency criteria for a class of convex functions connected with tangent function

Muhammad Ghaffar Khan; Sheza.M. El-Deeb; Daniel Breaz; Wali Khan Mashwani; Bakhtiar Ahmad; Muhammad Ghaffar Khan; Sheza.M. El-Deeb; Daniel Breaz; Wali Khan Mashwani; Bakhtiar Ahmad

doi:10.3934/math.2024906

AIMS Mathematics

2024, Volume 9, Issue 7: 18608-18624. doi: 10.3934/math.2024906

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Research article

Sufficiency criteria for a class of convex functions connected with tangent function

1.
Institute of Numerical Sciences, Kohat University of Sciences and Technology, Kohat 26000, Pakistan
2.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
4.
Department of Mathematics, "1 Decembrie 1918" University of Alba-Iulia, 510009 Alba Iulia, Romania
5.
Govt. Degree College Mardan, Pakistan

Received: 08 January 2024 Revised: 27 March 2024 Accepted: 02 April 2024 Published: 03 June 2024
MSC : 30C45, 30C50

The research here was motivated by a number of recent studies on Hankel inequalities and sharp bounds. In this article, we define a new subclass of holomorphic convex functions that are related to tangent functions. We then derive geometric properties like the necessary and sufficient conditions, radius of convexity, growth, and distortion estimates for our defined function class. Furthermore, the sharp coefficient bounds, sharp Fekete-Szegö inequality, sharp 2nd order Hankel determinant, and Krushkal inequalities are given. Moreover, we calculate the sharp coefficient bounds, sharp Fekete-Szegö inequality, and sharp second-order Hankel determinant for the functions whose coefficients are logarithmic.
- holomorphic convex functions,
- convolution,
- tangent function,
- Krushkal inequality,
- logarithmic coefficients
Citation: Muhammad Ghaffar Khan, Sheza.M. El-Deeb, Daniel Breaz, Wali Khan Mashwani, Bakhtiar Ahmad. Sufficiency criteria for a class of convex functions connected with tangent function[J]. AIMS Mathematics, 2024, 9(7): 18608-18624. doi: 10.3934/math.2024906

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Abstract

The research here was motivated by a number of recent studies on Hankel inequalities and sharp bounds. In this article, we define a new subclass of holomorphic convex functions that are related to tangent functions. We then derive geometric properties like the necessary and sufficient conditions, radius of convexity, growth, and distortion estimates for our defined function class. Furthermore, the sharp coefficient bounds, sharp Fekete-Szegö inequality, sharp 2nd order Hankel determinant, and Krushkal inequalities are given. Moreover, we calculate the sharp coefficient bounds, sharp Fekete-Szegö inequality, and sharp second-order Hankel determinant for the functions whose coefficients are logarithmic.

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