Biholomorphic mappings on bounded starlike circular domains

Let Ω ⊂ C n be a bounded starlike circular domain with 0 ∈ Ω . In this paper, we introduce a class of holomorphic mappings M g on Ω. Let f ( z ) be a normalized locally biholomorphic mapping on Ω such that J f − 1 ( z ) f ( z ) ∈ 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.