Third Hankel determinant for a subclass of close-to-star functions associated with exponential function

Abstract

In the present paper, we consider a subclass of close-to-star functions associated to exponential function, in the open unit disc $E=\{z\in \mathrm{ℂ}:|z|<1\}$. Here the main purpose is to establish the upper bound for the third Hankel determinant for this class. Also, we investigate the same bounds for two-fold and three-fold symmetric functions.