Third Hankel Determinant for A Class of Functions with Respect to Symmetric Points Associated with Exponential Function

Abstract

The purpose of the present work is to determine the possible upper bound of third order Hankel determinant for the functions starlike and convex with respect to symmetric points associated with exponential functions.

Coefficient Inequalities for Certain Subclass of Starlike Function with respect to Symmetric points related to q-exponential Function

“…Where the concepts of quantum calculus and q-derivative operator have been applied. The current study determined that on taking 𝑞𝑞 → 1 − for the result proved in this research article, similar results were obtained that were already proved in [47].…”

“…The current study is expanded by using quantum calculus and tends to investigate the upper bounds of the 3rd Hankel Determinant, for the classes of a star-like function with respect to symmetrical points subordinate to exponential functions. Mahmood et al [40] Shi et al [41], Verma et al [42], Viswanadh et al [43], Omer [44], Joshi et al [45], Breaz et al [46], Wang [47], and investigated the class of univalent function star-like with respect to symmetrical points. Here, the following subclass of starlike function are defined below: Definition 1.1.…”

Hankel Determinant for a Subclass of Starlike Functions with Respect to Symmetric Points Subordinate to the Exponential Function

“…s (e z ), then H 3,1 = 13 128 . Comparing references [31,33], it is evident that Zaprawa's research results improved upon some of Ganesh's conclusions.…”

“…In 2020, Ganesh et al introduced and investigated a class S * s (e z ) of analytic functions in [31], defined as follows:…”

On coefficient problems for functions starlike with respect to symmetric points

“…This class was first discussed by Ganesh et al in [3], where some coefficients functionals were estimated. The majority of results were not sharp.…”