Sharp distortion theorems for a subclass of close-to-convex mappings

Abstract

We introduce the class of strongly close-to-convex mappings of order α in the unit ball of a complex Banach space, and then, we give the sharp distortion theorems for this class of mappings in the unit ball of a complex Hilbert space X or the unit polydisc in ℂn. As an application, a sharp growth theorem for strongly close-to-convex mappings of order α is obtained.