The Study for. Some Subclasses of Biholomorphic Mappings by an Unified Method
LetOCn be a bounded starlike circular domain with 0O. In this paper, we introduce a class of holomorphic mappings Mg onO. Let f(z) be a normalized locally biholomorphic mapping onOsuch that Jf 1(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.