Convergence theorems for multivalued \(\phi\)-hemicontractive operators and \(\phi\)-strongly accretive operators
type: Item
instance of: scholarly article
title: Convergence theorems for multivalued \(\phi\)-hemicontractive operators and \(\phi\)-strongly accretive operators
zbMATH Open document ID: 1067.47079
DOI: 10.1016/S0898-1221(03)90183-0
author: Yanyan Li
publication date: 2004-09-23T00:00:00Z
review text: For a multivalued \(\Phi\)--hemicontractive operator \(T: E \rightarrow 2^E\) with bounded range on a uniformly smooth Banach space it is shown that, under suitable conditions, both the Ishikawa and Mann iteration processes defined by \textit{Y. Xu} [J. Math. Anal. Appl. 224, No. 1, 91--101 (1998; Zbl 0936.47041)] converge strongly to the unique fixed point of \(T\). A related result concerns the iterative solution of a multivalued \(\Phi\)-accretive operator equation.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 2102406
zbMATH Keywords: multivalued operators
zbMATH Keywords: Ishikawa iteration
zbMATH Keywords: uniformly smooth Banach space
zbMATH Keywords: \(\phi\)-strongly accretive operator
reviewed by: Werner C. Rheinboldt
MaRDI profile type: Publication
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full work available at URL: s0898-1221(03)90183-0
OpenAlex ID: W1985514919
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2102406