Shrinking projection algorithms for equilibrium problems with a bifunction defined on the dual space of a Banach space

Shrinking projection algorithms for finding a solution of an equilibrium problem with a bifunction defined on the dual space of a Banach space, in this paper, are introduced and studied. Under some suitable assumptions, strong and weak convergence results of the shrinking projection algorithms are e...

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Published inFixed point theory and applications (Hindawi Publishing Corporation) Vol. 2011; no. 1
Main Authors Chen, Jia-wei, Je Cho, Yeol, Wan, Zhongping
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 30.11.2011
Subjects
Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Topology
sunny generalized nonexpansive retraction
shrinking projection algorithm
fixed point
strong and weak convergence
equilibrium problem
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ISSN1687-1812
1687-1812
DOI10.1186/1687-1812-2011-91

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Abstract Shrinking projection algorithms for finding a solution of an equilibrium problem with a bifunction defined on the dual space of a Banach space, in this paper, are introduced and studied. Under some suitable assumptions, strong and weak convergence results of the shrinking projection algorithms are established, respectively. Finally, we give an example to illustrate the algorithms proposed in this paper. 2000 Mathematics Subject Classification: 47H09; 65J15; 90C99.
AbstractList Shrinking projection algorithms for finding a solution of an equilibrium problem with a bifunction defined on the dual space of a Banach space, in this paper, are introduced and studied. Under some suitable assumptions, strong and weak convergence results of the shrinking projection algorithms are established, respectively. Finally, we give an example to illustrate the algorithms proposed in this paper. 2000 Mathematics Subject Classification: 47H09; 65J15; 90C99.
ArticleNumber 91
Author Chen, Jia-wei
Wan, Zhongping
Je Cho, Yeol
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10.1007/978-3-662-00547-7
10.1016/j.jmaa.2007.09.062
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10.1016/0362-546X(91)90200-K
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10.1137/S105262340139611X
10.1016/j.na.2009.02.106
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Copyright Chen 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.
Copyright_xml – notice: Chen 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.
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Issue 1
Keywords sunny generalized nonexpansive retraction
shrinking projection algorithm
fixed point
strong and weak convergence
equilibrium problem
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SubjectTerms Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Topology
Title Shrinking projection algorithms for equilibrium problems with a bifunction defined on the dual space of a Banach space
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