用统一方法研究双全纯映射的一些子族

摘要

Let Ω ∈ Cn be a bounded starlike circular domain with 0 ∈Ω. In this paper,we introduce a class of holomorphic mappings Mg on Ω. Let f(z) be a normalized locally biholomorphic mapping on Ω such that J-1f(z)f(z) ∈Mg and z=0 is the zero of order k+1 of f(z) - z. We obtain the growth and covering theorems for f(z). Especially, as corollaries,we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of starlike mappings are shown.