Path convergence and approximation of common zeroes of a finite family of \(m\)-accretive mappings in Banach spaces
type: Item
instance of: scholarly article
title: Path convergence and approximation of common zeroes of a finite family of \(m\)-accretive mappings in Banach spaces
zbMATH Open document ID: 1206.47086
DOI: 10.1155/2010/285376
author: Y. Shehu
author: Jerry N. Ezeora
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/223988
review text: Summary: Let \(E\) be a real Banach space which is uniformly smooth and uniformly convex. Let \(K\) be a nonempty, closed and convex sunny nonexpansive retract of \(E\), where \(Q\) is the sunny nonexpansive retraction. If \(E\) admits weakly sequentially continuous duality mapping \(j\), path convergence is proved for a nonexpansive mapping \(T:K\rightarrow K\). As an application, we prove strong convergence to common zeroes of a finite family of \(m\)-accretive mappings of \(K\) to \(E\). As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings from \(K\) to \(E\) under certain mild conditions.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5791612
zbMATH Keywords: Banach space
zbMATH Keywords: path convergence
zbMATH Keywords: \(m\)-accretive mappings
zbMATH Keywords: pseudocontractive mappings
MaRDI profile type: Publication
Wikidata QID: Q58649806
OpenAlex ID: W1978238710
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description: scientific article; zbMATH DE number 5791612