A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of 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]College of Mathematics and Information Science, Henan University, Kaifeng 475001, China

出　　处：《Chinese Quarterly Journal of Mathematics》2007年第1期22-28,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 the Guangdong Natural Science Foundation(06301315);Supported by the Doctoral Foundation of Zhanjiang Normal University(Z0420);Supported by the Natural Science Foundation of Henan University(XK03YBSX200)

摘　　要：Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z1））^γnzn）1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=（z1,z2,…,zn）＇∈Cn：∑^n j=1｜zj｜^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers.

关 键 词：almost starlike mapping of order α starlike mapping generalized Roper- Surffridge extension operator 

分 类 号：O174.56[理学—数学]