An application of a random fixed point theorem to random best approximation
type: Item
instance of: scholarly article
title: An application of a random fixed point theorem to random best approximation
zbMATH Open document ID: 0956.47023
author: Ismat Beg
author: Nazeer Shahzad
published in: Archiv der Mathematik
publication date: 2001-02-27T00:00:00Z
review text: Let \(X\) be a Banach space and let \((\Omega, \mathcal{A})\) be a measurable space. Functions \(f,g\) from \(\Omega \times X \mapsto X\) are here called random operators. The authors show that if \(f\) anf \(g\) satisfy a long list of complicated conditions (impossible to summarize or explain here) then there is a mapping \(\xi\) from \(\Omega\) to a set \(P \subseteq X\) (\(P\) is the set of best approximations in a set \(S\) to a given point) with the property that \(\xi(\omega) = f(\omega, \xi(\omega)) = g(\omega, \xi(\omega))\) for all \(\omega \in \Omega\). Such a function \(\xi\) is here called a common random fixed point. The reviewer has the impression that, in any given instance, it may be easier to prove the result directly than verify the conditions of the theorem.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H40
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 1462960
zbMATH Keywords: best approximation
zbMATH Keywords: random fixed point
zbMATH Keywords: random operator
MaRDI profile type: Publication
full work available at URL: s000130050446
OpenAlex ID: W2028936972
DOI: 10.1007/S000130050446
description: scientific article; zbMATH DE number 1462960