Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings
type: Item
instance of: scholarly article
title: Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings
zbMATH Open document ID: 1086.47048
DOI: 10.1155/S0161171204308161
author: Safeer Hussain Khan
author: H. Fukhar-Ud-Din
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/52318
review text: Let \(C\) be a (nonempty) bounded closed convex subset of a Banach space \(E\) and \((S,T)\) be a pair of asymptotically nonexpansive selfmaps of \(C\). The weak and strong convergence of the iterative scheme \(x_{n+1}=(1-a_n)x_n+a_nS^ny_n+u_n,\) \(y_n=(1-b_n)x_n+b_nT^nx_n+v_n\) \((n\geq 1)\) is discussed; here, \((a_n)\), \((b_n)\) are sequences in \([0,1]\) and \((u_n)\), \((v_n)\) are sequences in \(E\) with \(\sum_n u_n, \sum_n v_n < \infty\).
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 49M05
zbMATH DE Number: 2171565
zbMATH Keywords: Banach space
zbMATH Keywords: closed bounded convex subset
zbMATH Keywords: nonexpansive map
zbMATH Keywords: iterative scheme with errors
zbMATH Keywords: common fixed point
zbMATH Keywords: strong convergence
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
OpenAlex ID: W2075547175
description: scientific article; zbMATH DE number 2171565