On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space

作     者：张文俊 刘太顺 

作者机构：Department of Mathematics Shenzhen University Normal College Shenzhen 518060 China Department of Mathematics Univ. of Sci. and Technol. of China Hefei 230026 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2002年第45卷第12期

页      面：1538-1547页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work was supported by 973 Project  the National Natural Science Foundation of China (Grant No. 19871081) and the Natural Science Foundation of Guangdong Province and Anhui Province. 

主　　题：Banach space, quasi-convex mapping, growth theorem, covering theorem. 

摘      要：A class of biholomorphic mappings named quasi-convex mapping is introduced in the unitball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class ofstarlike mappings and contains the class of convex mappings properly, and it has the same growth and coveringtheorems as the convex mappings. Furthermore, when the Banach space is confined to Cn, the quasi-convexmapping is exactly the quasi-convex mapping of type A introduced by K. A. Roper and T. J. Suffridge.