Differential Subordination of Certain Class of Starlike Functions

This paper presents several results concerning second and third-order differential subordination for the class ${\mathcal{S}}_e^{\ast }:=\{f\in \mathcal{A}:z{f}^{\mathrm{\prime }}(z)\mathrm{/}f(z)\prec e^z\}$, which represents the class of starlike functions associated with exponential function.