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 the second Hankel determinant problem for the class of close-to-convex functions related with the certain generalized starlike functions. Initiating with the definition of the class, specific preliminary lemmas was presented to attain the primary objective of this research. By addressing the second Hankel determinant problem for the class of close-to-convex functions and extending the findings to generalize results for other classes, this research not only contributes to the understanding of univalent functions but also holds the potential to enhance applications in diverse mathematical domains to offer valuable insights with practical implications.