Sharp growth and distortion theorems for a subclass of biholomorphic mappings

Let X be a complex Banach space with norm k k, and B be the unit ball in X. In this paper, we introduce a class of holomorphic mappings Mg on B. Let F .x/ be a normalized locally biholomorphic mapping on B such that .DF.x//􀀀1F .x/ 2 Mg . We investigate the sharp growth theorem for F .x/. As applications, the sharp distortion theorems for a subclass of starlike mappings are obtained.