ON THE GENERALIZED CLASS OF CLOSE-TO-CONVEX MAPPINGS

Abstract

In this paper, a class of holomorphic mappings is introduced in the unit ball of complex Banach space which is the extension of subclass of close-to-convex functions in $\mathbb{C}$, 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 $\mathbb{C}^n$ . As an application, a sharp growth theorem for this class is obtained. These results generalize many known results.