Strong convergence of iteration algorithms for a countable family of nonexpansive mappings
type: Item
instance of: scholarly article
title: Strong convergence of iteration algorithms for a countable family of nonexpansive mappings
zbMATH Open document ID: 1222.47119
author: Yisheng Song
author: Yunchun Zheng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-07-24T00:00:00Z
review text: For a countable family \(\{T_n\}_{n=1}^{+\infty}\) of nonexpansive mappings, the authors consider the iteration \(x_{n+1}=\alpha_nu+(1-\alpha_n)T_nx_n\) under the conditions (C1) lim\(_{n\rightarrow \infty} \alpha _n=0\) and (C2) \(\sum_{n=1}^\infty \alpha _n = \infty\). These are called modified Halpern iterations by some authors and are referred to as Halpern type iterations in the present paper. The authors prove several strong convergence theorems for such iterations and present examples as well as applications to equilibrium problems and variational inequalities for continuous monotone mappings.
reviewed by: Aleksandar Perović
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5586841
zbMATH Keywords: countable family of nonexpansive mappings
zbMATH Keywords: modified Halpern iteration
zbMATH Keywords: uniformly Gâteaux differentiable norm
zbMATH Keywords: reflexive Banach space
zbMATH Keywords: strong convergence
MaRDI profile type: Publication
full work available at URL: j.na.2009.01.219
OpenAlex ID: W2090702409
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DOI: 10.1016/J.NA.2009.01.219
description: scientific article; zbMATH DE number 5586841