Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces
type: Item
instance of: scholarly article
title: Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces
zbMATH Open document ID: 1218.47131
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-04-30T00:00:00Z
review text: Let \(C\) be a nonempty closed convex subset of a real Banach space \(X\) whose norm is uniformly Gâteaux differentiable and let \(T : C\to C\) be a continuous pseudocontraction with nonempty fixed point set \(F(T)\). A sequence \((x_n)\) is defined iteratively which converges strongly to a fixed point of \(T\). For all the continuous pseudocontractive mappings for which it is possible to construct the sequence \((x_n)\), the obtained result improves and extends a recent result of \textit{Y.-H. Yao}, \textit{Y.-C. Liou} and \textit{R.-D. Chen} [Nonlinear Anal., Theory Methods Appl. 67, No.~12, A, 3311--3317 (2007; Zbl 1129.47059)].
reviewed by: Stepan Agop Tersian
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 5550325
zbMATH Keywords: explicit iterative algorithm
zbMATH Keywords: pseudo-contraction
zbMATH Keywords: fixed point
zbMATH Keywords: strong convergence theorem
zbMATH Keywords: Banach space.
author: Haiyun Zhou
MaRDI profile type: Publication
full work available at URL: j.na.2008.08.012
OpenAlex ID: W2025453475
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DOI: 10.1016/J.NA.2008.08.012
description: scientific article; zbMATH DE number 5550325