Random approximations and fixed point theorems
type: Item
instance of: scholarly article
title: Random approximations and fixed point theorems
zbMATH Open document ID: 0843.47035
author: Xun Luo
author: Gang Li
author: George Xian-Zhi Yuan
published in: Journal of Approximation Theory
publication date: 1996-08-18T00:00:00Z
review text: This paper deals with stochastic versions of the best approximation theorem of \textit{K. Fan} [Math. Z. 112, 234-240 (1969; Zbl 0185.39503)] which states that for any \(E\)-valued continuous map defined on a compact, convex subset \(X\) of a normed space \(E\) there exists \(u\in X\) such that \(\text{dist}(f(u), X)= |u- f(u)|\). The authors obtain their random best approximation theorems for single valued and set-valued mappings by the use of random variational inequalities. Random fixed point theorems are then derived. The paper contains a rather comprehensive and useful reference list of 38 items.
reviewed by: Raymond Mortini
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H40
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 847524
zbMATH Keywords: stochastic versions of the best approximation theorem
zbMATH Keywords: set-valued mappings
zbMATH Keywords: random variational inequalities
MaRDI profile type: Publication
full work available at URL: jath.1996.0014
OpenAlex ID: W2041964837
DOI: 10.1006/JATH.1996.0014
description: scientific article; zbMATH DE number 847524