Weak convergence to a fixed point of the sequence of Mann type iterates
type: Item
instance of: scholarly article
title: Weak convergence to a fixed point of the sequence of Mann type iterates
zbMATH Open document ID: 0811.47067
author: Jong Yeoul Park
author: Jae Ug Jeong
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-08-17T00:00:00Z
review text: The authors prove the following theorem: Let \(T\) be a quasi-nonexpansive self-mapping of a closed convex subset of a uniformly convex Banach space satisfying Opial's condition with \(I-T\) demiclosed with respect to zero. Then the sequence \(\{x_ n\}_{n=1}^ \infty\) defined by \(x_{n+1}= (1- \alpha_ n) x_ n+ \alpha_ n Tx_ n\) converges weakly to some fixed point of \(T\). A similar result is obtained for continuous generalized nonexpansive mappings.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 617442
zbMATH Keywords: quasi-nonexpansive self-mapping of a closed convex subset of a uniformly convex Banach space
zbMATH Keywords: Opial's condition
zbMATH Keywords: continuous generalized nonexpansive mappings
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1184
OpenAlex ID: W2093991524
DOI: 10.1006/JMAA.1994.1184
Recommended article: Convergence of modified Mann type of iterates and fixed point
Recommended article: Mann iteration of weak convergence theorems in Banach space
Recommended article: WEAK AND STRONG CONVERGENCE OF MANN'S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS
Recommended article: Q3132124
Recommended article: Convergence of Mann Type Iterative Sequence for Asymptotically \mbox{\boldmath $\phi$}-hemicontrative Type Mapping Pair
Recommended article: On the convergence of Mann iterates to a common fixed point for a pair of mappings
Recommended article: Q4720284
Recommended article: Q4553773
Recommended article: Strong convergence of Mann type doubly sequence iterations with applications
Recommended article: Q3512738
description: scientific article; zbMATH DE number 617442