数学物理学报 ›› 2015, Vol. 35 ›› Issue (6): 1127-1135.

• 论文 • 上一篇    下一篇

非光滑有界凸域上全纯自映射的随机迭代

杨利琴1, 邓方文2   

  1. 1 武汉海事职业学院 武汉 430311;
    2 中国科学院武汉物理与数学研究所 武汉 430071
  • 收稿日期:2015-05-07 修回日期:2015-10-19 出版日期:2015-12-25 发布日期:2015-12-25
  • 通讯作者: 邓方文,fwdeng@wipm.ac.cn E-mail:fwdeng@wipm.ac.cn
  • 作者简介:杨利琴,yangliqin11@yeah.com
  • 基金资助:

    国家自然科学基金(11271359)资助

Random Iteration of Holomorphic Self-Maps on Non-Smooth Bounded Convex Domain

Yang Liqin1, Deng Fangwen2   

  1. 1 Wuhan Maritime Vocational College, Wuhan 430311;
    2 Wuhan Insitute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071
  • Received:2015-05-07 Revised:2015-10-19 Online:2015-12-25 Published:2015-12-25

摘要:

该文在经典的Wolff-Denjoy理论的基础上研究Cn中有界严格凸域与有界弱凸域上随机迭代的收敛性问题.给出了有界严格凸域中全纯映射的随机迭代存在内闭一致收敛到边界上的常值映射的子序列的限制条件;而在有界弱凸域中,所给的限制条件强了很多,但全纯映射的随机迭代的收敛性却减弱了.该文所给定理的证明方法可以证明单个解析函数的相应结果的迭代理论.

关键词: 随机迭代, 有界凸域, 收敛性, 全纯映射

Abstract:

In this paper, we study random iterative convergence problem on bounded strictly convex and bounded weak convex domain in Cn based on the classical Wolff-Denjoy theorem. On bounded strictly convex domain, we prove that there exists a supsequence which converges uniformly to constant map on the boundary under some condition. On bounded weak convex domain, the restrictive condition becomes stronger, but the convergence result becomes weaker. The method in this paper can be used to prove the iterative theorem of single analytic function.

Key words: Random iteration, Bounded convex domain, Convergence, Holomorphic map

中图分类号: 

  • O1-0