Hankel determinant for certain new classes of analytic functions associated the activation functions

YueJuan Sun; Muhammad Arif; Khalil Ullah; Lei Shi; Muhammad Imran Faisal

doi:10.1016/j.heliyon.2023.e21449

Hankel determinant for certain new classes of analytic functions associated the activation functions

Heliyon. 2023 Oct 27;9(11):e21449. doi: 10.1016/j.heliyon.2023.e21449. eCollection 2023 Nov.

Authors

YueJuan Sun¹, Muhammad Arif², Khalil Ullah², Lei Shi³, Muhammad Imran Faisal⁴

Affiliations

¹ School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, Henan, P.R. China.
² Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan.
³ School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, Henan, P.R. China.
⁴ Department of Mathematics, Taibah University, Universities Road, PO Box: 344, Medina, Saudi Arabia.

Abstract

In this article, we introduce two new classes of analytic functions $J_{t a n h}$ and $J_{S G}$ which are associated with the activation functions and defined by the ratio of analytic representations of convex and starlike functions. For functions in these classes, our primary goal is to determine the sharp upper bounds of second and third Hankel determinants.

Keywords: 30C45; 30C80; Activation functions; Coefficient bounds; Hankel determinant; Univalent mappings.