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 $S_e^{\ast }=\{f(z)\in S:z{f}^{\prime }(z)/f(z)\prec e^z,(z\in \mathbb{D})\}$ was introduced and studied by Mendiratta $et$ $al.$ ~\cite{mendiratta2015subclass}. In this article, we obtain sharp bound for third Hankel determinant for the class $S_e^{\ast }$, 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.

There is calculation error in the main theorem. We are working on it for rectification, in the mean-time the paper is withdrawn