The convergence property of Ishikawa iteration schemes in noncompact subsets of Hilbert spaces and its applications to complementarity theory
type: Item
instance of: scholarly article
title: The convergence property of Ishikawa iteration schemes in noncompact subsets of Hilbert spaces and its applications to complementarity theory
zbMATH Open document ID: 1078.47049
publication date: 2005-03-08T00:00:00Z
review text: Let \(K\) be a closed convex subset of a Hilbert space and \(T:K \to K\) some nonexpansive map. Sufficient conditions are given for the Ishikawa iteration scheme \(x_{n+1}= (1-\alpha_n)x_n+\alpha_nT((1-\beta_n)x_n+\beta_nTx_n)\) to be convergent towards a fixed point of \(T\). Applications to complementarity theorems are also discussed.
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47N10
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 2142425
zbMATH Keywords: Ishikawa iteration schemes
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: completely continuous mapping
zbMATH Keywords: fixed point
zbMATH Keywords: nonlinear complementarity problems
zbMATH Keywords: variational inequalities as variational inclusions
zbMATH Keywords: closed convex set
author: G. Isac
author: Jinlu Li
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.06.018
OpenAlex ID: W2024162818
cites work: Mean Value Methods in Iteration
cites work: Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
cites work: Krasnoselski-Mann Iterations in Normed Spaces
cites work: Geometric properties of Banach spaces and nonlinear iterations
cites work: A note on Mann iteration for quasi-nonexpansive mappings
cites work: On the Mann Iterative Process
cites work: A convergence theorem of the sequence of Ishikawa iterates for quasi- contractive mappings
cites work: Convergence of Ishikawa and Mann iteration schemes for asequence of selfmaps in a Hilbert space
cites work: A note on the Ishikawa iteration scheme
cites work: The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings
cites work: An iterative process for nonlinear Lipschitzian strongly accretive mappings in \(L_ p\) spaces
cites work: Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions
cites work: Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
cites work: Existence and approximation of solutions to variational inclusions with accretive mappings in Banach spaces.
cites work: Q4003375
cites work: Complementarity problems
cites work: Topological methods in complementarity theory
cites work: Leray-Schauder type alternatives and the solvability of complementarity problems
cites work: Q4045174
cites work: Q4464213
cites work: Global bifurcation in variational inequalities: applications to obstacle and unilateral problems
DOI: 10.1016/J.CAMWA.2004.06.018
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142425