The second and third Hankel determinants for starlike and convex functions associated with Three-Leaf function

Amina Riaz; Mohsan Raza; Muhammad Ahsan Binyamin; Afis Saliu

doi:10.1016/j.heliyon.2022.e12748

The second and third Hankel determinants for starlike and convex functions associated with Three-Leaf function

Heliyon. 2023 Jan 10;9(1):e12748. doi: 10.1016/j.heliyon.2022.e12748. eCollection 2023 Jan.

Authors

Amina Riaz¹, Mohsan Raza², Muhammad Ahsan Binyamin², Afis Saliu³

Affiliations

¹ Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan.
² Department of Mathematics, Government College University Faisalabad, Pakistan.
³ Department of Mathematics, University of the Gambia, Birkama Campus, MDI Road, Kanifing Serrekunda P.O. Box 3530, the Gambia.

Abstract

In this paper, we give sharp bounds of the Hankel determinant $H_{2} (3) (f)$ for the coefficients of functions in the class of starlike functions related to a domain that is like three leaves. We also give sharp bounds for the Hankel determinants $H_{3} (1) (f)$ and $H_{2} (3) (f)$ for the coefficients of functions in the class of convex functions related to the three-leaf-like domain.

Keywords: Convex function; Hankel determinants; Starlike function; Three-leaf function; Univalent function.