Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (6): 1127-1135.

Previous Articles     Next Articles

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

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

CLC Number: 

  • O1-0
Trendmd