Second Hankel Determinants for a Subclass of Close-to-Convex Function Related to Certain Generalized Keobe Function

Abstract

For ages, researchers have conducted numerous studies exploring every aspect of problems related to univalent functions. Most of the research has been concentrated on investigating the diverse properties of univalent functions. Notably, finding the upper bound of Hankel determinants has become an intriguing problem among researchers in this field. The aim of this paper is to solve on the second Hankel determinant problem for the class k z β ( ) C of close-to-convex functions related with the certain generalized starlike functions. We first give the definition of the class k z β ( ) C and use certain preliminary lemmas to achieve on the main goal of this research. The finding of this research generalizes certain results related to the second Hankel determinant of other classes of close-to-convex functions.