Univalence of certain integral operators

Abstract

Let $ { \cal A}_n$ be the class of functions $ f(z) $ which are analytic and $ n $-fold symmetric in the open unit disk $ {\Bbb U} $. The integral operator $ G_\alpha(z) $ for $ f(z)\in {\cal A}_n $ is considered. The object of the present paper is to derive univalence conditions of the integral operator $G_\alpha(z)$ for $ f(z)\in {\cal A}_n$.