Random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces
type: Item
instance of: scholarly article
title: Random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces
zbMATH Open document ID: 0933.46040
author: Kazimierz Włodarczyk
author: Joanna Gonicka
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-10-25T00:00:00Z
review text: The authors prove a version of the Denjoy-Wolff theorem concerning convergence of iterates of analytic functions from a domain into itself. The context here is for an unbounded domain \(G\) in a sequentially complete locally convex space \(E\), and for an arbitrary sequence \((f_n)\) of functions which map \(G\) into a domain \(D\) which is strictly inside \(G\). The result then is that under additional technical conditions the sequence of iterates \((f_1\circ\cdots\circ f_n)_n\) converges to a constant map. Several comments are made which show that the result fails without the imposition of various additional hypotheses. The authors also discuss a generalization of this result to uniform spaces, and they also give a helpful list of references to earlier work in this classical area.
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 1332889
zbMATH Keywords: holomorphic contractions
zbMATH Keywords: Denjoy-Wolff theorem
zbMATH Keywords: convergence of iterates of analytic functions
reviewed by: Richard M. Aron
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6397
OpenAlex ID: W1971676253
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DOI: 10.1006/JMAA.1999.6397
description: scientific article; zbMATH DE number 1332889