Approximating solutions of variational inequalities for asymptotically nonexpansive mappings
type: Item
instance of: scholarly article
title: Approximating solutions of variational inequalities for asymptotically nonexpansive mappings
zbMATH Open document ID: 1181.65098
author: Chi Kin Chan
author: Shihsen Chang
author: H. W. Joseph Lee
author: J. K. Kim
published in: Applied Mathematics and Computation
publication date: 2009-06-24T00:00:00Z
review text: Let \(E\) be a real Banach space with a uniformly Gâteaux differentiable norm and possessing a uniform normal structure. Iterative sequences are constructed which involve a contractive and an asymptotically nonexpanding mappings \(K\to K\), where \(K\) is a bounded closed convex subset of \(E\). Conditions are given for convergence of these sequences to a fixed point which is also the unique solution of some variational inequalities. Thus previous results on asymptotically nonexpanding mappings are generalized [see e.g. \textit{C.~Chidume, J.~Li} and \textit{A.~Udomene}, Proc. Am. Math. Soc. 133, No.~2, 473--480 (2005; Zbl 1073.47059)].
Mathematics Subject Classification ID: 65K15
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 5569540
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: fixed point
zbMATH Keywords: uniform normal structure
zbMATH Keywords: iscosity approximation
zbMATH Keywords: uniformly Gâteaux differentiable norm
zbMATH Keywords: normalized duality mapping
zbMATH Keywords: Banach space
zbMATH Keywords: convergence
zbMATH Keywords: variational inequalities
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
full work available at URL: j.amc.2009.01.078
OpenAlex ID: W2050040532
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DOI: 10.1016/J.AMC.2009.01.078
description: scientific article; zbMATH DE number 5569540