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

Abstract: Recently, the subclass of starlike functions associated with exponential function $e<sup>z$, given by ${S}^*_e = {f(z)\in {S}:{zf&#39;(z)}/{f(z)} \prec e^z, (z\in \mathbb{D}) }$ was introduced and studied by Mendiratta $et$ $al.$ ~\cite{mendiratta2015subclass}. In this article, we obtain sharp bound for third Hankel determinant for the class $S_e<sup>\ast$, by improving the already known results, in this direction. In our methodology, we use the newly obtained expression for the fourth coefficient of Carath\'{e}odory functions.