Biholomorphic mappings on bounded starlike circular domains

被引:8
作者
Xu, Qing-Hua [1 ]
Liu, Tai-Shun [2 ]
机构
[1] JiangXi Normal Univ, Coll Math & Informat Sci, Nanchang 330027, Peoples R China
[2] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China
关键词
Growth and covering theorem; Starlike mapping; Subclasses of starlike mappings; Zero of order k+1; PARAMETRIC REPRESENTATION; COEFFICIENT BOUNDS; COMPLEX-VARIABLES; GROWTH THEOREMS; SHARP GROWTH; C-N;
D O I
10.1016/j.jmaa.2009.12.025
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let Omega subset of C(n) be a bounded starlike circular domain With 0 is an element of Omega. In this paper, we introduce a class of holomorphic mappings M(g) on Omega. Let f(z) be a normalized locally biholomorphic mapping on Omega Such that integral(-1)(f) (z)f(z) is an element of 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. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码:153 / 163
页数:11
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