Third Hankel Determinant For A Class Of Starlike Functions Associated With Exponential Function

Abstract

Recently, the subclass of starlike functions associated with exponential function e z , given by S * e = {f (z) ∈ S : zf ′ (z)/f (z) ≺ e z , (z ∈ D)} was introduced and studied by Mendiratta et al. [16]. In this article, we obtain sharp bound for third Hankel determinant for the class S * e , by improving the already known results, in this direction. In our methodology, we use the newly obtained expression for the fourth coefficient of Carathéodory functions. Univalent functions; Starlike functions; Hankel determinant; Sharp bound; Exponential function.

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

“…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.…”