Abstract: Let Ω∈Cⁿ be a bounded starlike circular domain with 0∈Ω. In this paper, we introduce a class of holomorphic mappings M_g onΩ. Let f(z) be a normalized locally biholomorphic mapping onΩsuch 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 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. 

Key words: growth , and , covering , theorem;starlike , mapping;subclasses , of starlike , mappings;zero of order k+1