Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems

In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known me...

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Published inFixed point theory and algorithms for sciences and engineering Vol. 2011; no. 1; pp. 1 - 10
Main Authors Yao, Yonghong, Liou, Yeong-Cheng, Wong, Mu-Ming, Yao, Jen-Chih
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 17.09.2011
Springer Nature B.V
BioMed Central Ltd
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Classification
Convergence
CQ method
Differential Geometry
extragradient method
fixed point problems; monotone mapping
Fixed points (mathematics)
Inequalities
Iterative methods
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
nonexpansive mapping
projection
Sequences
Topology
variational inequality problem
nonexpansive mapping
projection
extragradient method
method
variational inequality problem
fixed point problems; monotone mapping
Online AccessGet full text
ISSN1687-1812
1687-1820
1687-1812
2730-5422
DOI10.1186/1687-1812-2011-53

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Abstract In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. Under some mild conditions, we prove the strong convergence of the sequences generated by the proposed method. Mathematics Subject Classification (2000): 47H05; 47H09; 47H10; 47J05; 47J25.
AbstractList In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. Under some mild conditions, we prove the strong convergence of the sequences generated by the proposed method. Mathematics Subject Classification (2000): 47H05; 47H09; 47H10; 47J05; 47J25.
In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. Under some mild conditions, we prove the strong convergence of the sequences generated by the proposed method. Mathematics Subject Classification (2000): 47H05; 47H09; 47H10; 47J05; 47J25.[PUBLICATION ABSTRACT]
Abstract In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. Under some mild conditions, we prove the strong convergence of the sequences generated by the proposed method. Mathematics Subject Classification (2000): 47H05; 47H09; 47H10; 47J05; 47J25.
In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. Under some mild conditions, we prove the strong convergence of the sequences generated by the proposed method.Mathematics Subject Classification (2000): 47H05; 47H09; 47H10; 47J05; 47J25.
ArticleNumber 53
Author Liou, Yeong-Cheng
Wong, Mu-Ming
Yao, Yonghong
Yao, Jen-Chih
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CitedBy_id crossref_primary_10_1007_s40306_014_0071_2
crossref_primary_10_1186_1687_1812_2012_15
crossref_primary_10_1007_s10013_013_0027_1
Cites_doi 10.1016/j.jmaa.2006.01.091
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ContentType Journal Article
Copyright Yao et al; licensee Springer. 2011. 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 ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Springer International Publishing AG 2011
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Keywords nonexpansive mapping
projection
extragradient method
method
variational inequality problem
fixed point problems; monotone mapping
Language English
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Snippet In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality...
Abstract In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational...
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SubjectTerms Analysis
Applications of Mathematics
Classification
Convergence
CQ method
Differential Geometry
extragradient method
fixed point problems; monotone mapping
Fixed points (mathematics)
Inequalities
Iterative methods
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
nonexpansive mapping
projection
Sequences
Topology
variational inequality problem
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Title Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems
URI https://link.springer.com/article/10.1186/1687-1812-2011-53
https://www.proquest.com/docview/1017669381
https://www.proquest.com/docview/1439744299
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https://doaj.org/article/f7bc198eaf58449da306d9d7f271d1e8
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