Convergences of nonexpansive iteration processes in Banach spaces
type: Item
instance of: scholarly article
title: Convergences of nonexpansive iteration processes in Banach spaces
zbMATH Open document ID: 1031.47046
DOI: 10.1016/S0022-247X(02)00228-7
author: Jong Soo Jung
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: Let \(T_i : E \rightarrow E\), \(i = 1, \dots, k\), be nonexpansive mappings on a reflexive Banach space \(E\) with a uniformly \(G\)-differentiable norm. The author considers the iteration \(x_{n+1} = (\alpha_0 I + \alpha_1 T_1 + \cdots \alpha_k T_k) x_n\) with \(\alpha_i \geq 0\), \(\alpha_0 > 0\), \(\alpha_0 + \cdots + \alpha_k = 1\), and proves a dual weak almost convergence result which is then used to obtain the weak convergence of the process.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1866604
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: dual weak almost convergence
zbMATH Keywords: weak convergence
reviewed by: Werner C. Rheinboldt
MaRDI profile type: Publication
cites work: Q3213662
cites work: Strong convergence theorems for accretive operators in Banach spaces
cites work: On successive approximations for nonexpansive mappings in Banach spaces
cites work: A contribution to the theory of divergent sequences
cites work: Approximating fixed points of nonexpansive and generalized nonexpansive mappings
cites work: Weak convergence of the sequence of successive approximations for nonexpansive mappings
cites work: Product formulas, nonlinear semigroups, and accretive operators
cites work: Approximating Fixed Points of Nonexpansive Mappings
full work available at URL: s0022-247x(02)00228-7
OpenAlex ID: W2072109886
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description: scientific article; zbMATH DE number 1866604