The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems

ABSTRACT: In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α-inv...

Descripción completa

Detalles Bibliográficos
Autores principales: Saewan, Siwaporn, Kumam, Poom
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing AG 2012
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3656239/
https://www.ncbi.nlm.nih.gov/pubmed/23687626
http://dx.doi.org/10.1186/2193-1801-1-8
_version_ 1782270005017051136
author Saewan, Siwaporn
Kumam, Poom
author_facet Saewan, Siwaporn
Kumam, Poom
author_sort Saewan, Siwaporn
collection PubMed
description ABSTRACT: In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature.
format Online
Article
Text
id pubmed-3656239
institution National Center for Biotechnology Information
language English
publishDate 2012
publisher Springer International Publishing AG
record_format MEDLINE/PubMed
spelling pubmed-36562392013-05-17 The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems Saewan, Siwaporn Kumam, Poom Springerplus Research ABSTRACT: In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature. Springer International Publishing AG 2012-07-13 /pmc/articles/PMC3656239/ /pubmed/23687626 http://dx.doi.org/10.1186/2193-1801-1-8 Text en © Saewan and Kumam; licensee Springer. 2012 This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research
Saewan, Siwaporn
Kumam, Poom
The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
title The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
title_full The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
title_fullStr The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
title_full_unstemmed The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
title_short The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
title_sort hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3656239/
https://www.ncbi.nlm.nih.gov/pubmed/23687626
http://dx.doi.org/10.1186/2193-1801-1-8
work_keys_str_mv AT saewansiwaporn thehybridblockiterativealgorithmforsolvingthesystemofequilibriumproblemsandvariationalinequalityproblems
AT kumampoom thehybridblockiterativealgorithmforsolvingthesystemofequilibriumproblemsandvariationalinequalityproblems
AT saewansiwaporn hybridblockiterativealgorithmforsolvingthesystemofequilibriumproblemsandvariationalinequalityproblems
AT kumampoom hybridblockiterativealgorithmforsolvingthesystemofequilibriumproblemsandvariationalinequalityproblems

Ejemplares similares