Continuous dependence of attractors of iterated function systems
type: Item
instance of: scholarly article
title: Continuous dependence of attractors of iterated function systems
zbMATH Open document ID: 0862.54033
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-08-29T00:00:00Z
review text: The author observes that in the book [\textit{M. Barnsley}, Fractals everywhere (1988; Zbl 0691.58001)] the proof of a true theorem concerning the continuous dependence of the attractors on the parameter is based on a false lemma. He extends the result in question showing among others that the assumption of compactness of the parameter space is superfluous. Moreover he proves that a Banach space is finite-dimensional if, and only if, whenever a sequence of its contraction selfmaps converges pointwise to a contraction mapping \(A\), then the sequence of their fixed points converges to the fixed point of \(A\).
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 902496
zbMATH Keywords: Hausdorff metric
zbMATH Keywords: iterated function system
zbMATH Keywords: continuous dependence on parameter
zbMATH Keywords: contraction mapping
author: J. Jachymski
reviewed by: Janusz Matkowski
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0077
OpenAlex ID: W2012024795
DOI: 10.1006/JMAA.1996.0077
description: scientific article; zbMATH DE number 902496