The Subordination Principle and Its Application to the Generalized Roper-Suffridge Extension Operator

被引:0
作者
Jianfei Wang
Xiaofei Zhang
机构
[1] Huaqiao University,School of Mathematical Sciences
[2] Pingdingshan University,School of Mathematics and Statistics
来源
Acta Mathematica Scientia | 2022年 / 42卷
关键词
Biholomorphic mappings; starlike mappings; subordination; Loewner chain; 32H02; 30C45;
D O I
暂无
中图分类号
学科分类号
摘要
This note is devoted to applying the principle of subordination in order to explore the Roper-Suffridge extension operator and the Pfaltzgraff-Suffridge extension operator with special analytic properties. First, we prove that both the Roper-Suffridge extension operator and the Pfaltzgraff-Suffridge extension operator preserve subordination. As applications, we obtain that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta \in [0,1],\gamma \in [0,{1 \over r}]$$\end{document} and β+γ ≤ 1, then the Roper-Suffridge extension operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Phi _{\beta,\gamma }}(f)(z) = \left( {f({z_1}),{{\left( {{{f({z_1})} \over {{z_1}}}} \right)}^\beta }{{({f^\prime }({z_1}))}^\gamma }w} \right),\,\,z \in {\Omega _{p,r}}$$\end{document}
引用
收藏
页码:611 / 622
页数:11
相关论文
共 57 条
[1]  
Roper K A(1995)Convex mappings on the unit ball of ℂ J Anal Math 65 333-347
[2]  
Suffridge T J(2000)Univalent mappings associated with the Roper-Suffridge extension operator J Anal Math 81 331-342
[3]  
Graham I(2018)The Roper-Suffridge extension operator and its applications to convex mappings in ℂ Trans Amer Math Soc 11 2743-2759
[4]  
Kohr G(2002)Extension operators for locally univalent mappings Michigan Math J 50 37-55
[5]  
Wang J F(2008)The generalized Roper-Suffridge extension operator Acta Math Sci 28B 63-80
[6]  
Liu T S(2006)The generalized Roper-Suffridge extension operator for some biholomorphic mappings J Math Anal Appl 324 604-614
[7]  
Graham I(2006)Loewner chains associated with the generalized Roper-Suffridge extension operator J Math Anal Appl 322 107-120
[8]  
Hamada H(2002)On Roper-Suffridge extension operator J Anal Math 88 397-404
[9]  
Kohr G(2003)The generalized Roper-Suffridge extension operator J Math Anal Appl 284 425-434
[10]  
Feng S X(2008)Spirallike mappings and univalent subordination chains in ℂ Ann Sc Norm Super Pisa Cl Sci 7 717-740