On coeffcient estimates for a class of holomorphic mappings  

作　　者：XU QingHua1 & LIU TaiShun2 1 College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330027, China 2 Department of Mathematics, Huzhou Teacher’s College, Huzhou 313000, China 

出　　处：《Science China Mathematics》2009年第4期677-686,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10571164);Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20050358052);the Jiangxi Provincial Natural Science Foundation of China (Grant No. 2007GZS0177);Specialized Research Fund for the Doctoral Program of Jiangxi Normal University

摘　　要：Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))-1f(x) ∈ Mg and f(x) - x has a zero of order k + 1 at x = 0. We obtain coeffcient estimates for f(x). These results unify and generalize many known results.Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))-1f(x) ∈ Mg and f(x) - x has a zero of order k + 1 at x = 0. We obtain coeffcient estimates for f(x). These results unify and generalize many known results.

关 键 词：ZERO of order k + 1 coeffcient ESTIMATES the FORMULA of Faàdi BRUNO 

分 类 号：O174.52[理学—数学]