Viscosity approximation methods for fixed-points problems
type: Item
instance of: scholarly article
title: Viscosity approximation methods for fixed-points problems
zbMATH Open document ID: 0957.47039
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-03-08T00:00:00Z
review text: The main result of the paper is: Let \(C\) be a closed convex set of a real Hilbert space \(X\) and \(P:C\rightarrow C\) a nonexpansive operator so that its fixed point set \(S\) is nonempty. Given a sequence of positive real numbers \(\varepsilon_{n}\rightarrow 0\) and a contraction \(\pi:C\rightarrow C,\) the sequence \(x_{n}\in C\) given by the unique fixed point in \(C\) of the contraction \(\frac{1}{1+\varepsilon_{n}}P+\frac{\varepsilon_{n}} {1+\varepsilon_{n}}\pi\) strongly converges to the unique fixed point in \(S\) of the operator proj\(_{S}\circ\pi.\) Applications are given to viscosity principles for optimization problems and inclusions for monotone operators.
reviewed by: Mira-Cristiana Anisiu
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1423868
zbMATH Keywords: nonexpansive mappings
zbMATH Keywords: fixed point approximation
zbMATH Keywords: contraction
zbMATH Keywords: viscosity principles for optimization problems
zbMATH Keywords: inclusions for monotone operators
author: Abdellatif Moudafi
MaRDI profile type: Publication
OpenAlex ID: W2070694134
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DOI: 10.1006/JMAA.1999.6615
description: scientific article; zbMATH DE number 1423868