Biholomorphic mappings on bounded starlike circular domains

Let Omega subset of C(n) be a bounded starlike circular domain With 0 is an element of Omega. In this paper, we introduce a class of holomorphic mappings M(g) on Omega. Let f(z) be a normalized locally biholomorphic mapping on Omega Such that integral(-1)(f) (z)f(z) is an element of M(g) and z = 0 is the zero of order k + 1 of f(z) - z. We obtain a sharp growth theorem and sharp coefficient bounds for f(z). As applications, sharp distortion theorems for a subclass of starlike mappings are obtained. These results unify and generalize many known results. (C) 2009 Elsevier Inc. All rights reserved.