Random iterations, fixed points and invariant CRF-horospheres in complex Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:295

Article

Wlodarczyk, K ; Klim, D

关键词: holomorphic noncontractive map;    unbounded domain;    complex Banach space;    random iteration;    fixed point;    invariant CRF-horosphere;    Julia's lemma;    Wolff's theorem;   

DOI  :  10.1016/j.jmaa.2003.10.054

来源: Elsevier

【 摘 要 】

For holomorphic noncontractive maps on (not necessarily bounded) domains in complex Banach spaces, we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations. In particular, we show that the problem, concerning the existence of the horospheres determined by Caratheodory-Reiffen-Finsler pseudometrics defined on unbounded domains, has the solution and we prove new results of type of Julia's lemma and Wolff's theorem. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free