Growth and distortion theorems for a subclass of holomorphic mappings
نویسندگان
چکیده
Let X be a complex Banach space with norm ∥ · ∥, B be the unit ball in X. In this paper, we introduce a class of holomorphic mappings Mg on B. Let f(x) be a normalized locally biholomorphic mappings on B such that (Df(x))−1f(x) ∈ Mg and x = 0 is the zero of order k + 1 of f(x)− x. We investigate the growth theorem for f(x). As applications, the distortion theorems for the Jacobian matrix Jf (z) are obtained, where f(z) belongs to the subclasses of starlike mappings defined on the unit polydisc Dn in Cn. These results unify and generalize many known results.
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تاریخ انتشار 2013