A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α  

作　　者：LIU Xiao-song FENG Shu-xia 

机构地区：[1]School of Mathematics and Computation Science, Zhanjiang Normal University, Zhanjiang 524048, China [2]Institute of Mathematics, Henan University, Kaifeng 475001, China College of Mathematics and Information Science, Henan University, Kaifeng 475001, China

出　　处：《Chinese Quarterly Journal of Mathematics》2009年第2期310-316,共7页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China（10626015, 10571044）; Supported by Guangdong Natural Science Foundation（06301315）; Supported by the doctoral foundation of Zhanjiang Normal University（Z0420）

摘　　要：Suppose f is a spirallike function of type β and order α on the unit disk D.Let Ωn,p1,p2,…,pn={z=（z2,z2,…,zn）′∈C^n：∑j=1^n｜zj）^Pj〈1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers.In this paper,we will prove that Φn,β2,γ2,…βn,γn（f）（z）=（f（z1）, preserves spirallikeness of type β and order α on Ωn,p1,p2,…,Pn.

关 键 词：K spirallike mapping of type β and order β starlike mapping of order α gener-alized Roper-Suffridge extension operator 

分 类 号：O189.11[理学—数学] D90[理学—基础数学]