Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi- ϕ -nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex B...

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Published inFixed point theory and applications (Hindawi Publishing Corporation) Vol. 2011; no. 1; pp. 1 - 15
Main Author Kim, Jong Kyu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 24.06.2011
BioMed Central Ltd
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Asymptotic properties
Asymptotically quasi-ϕ-nonexpansive mapping
Banach space
Classification
Convergence
Differential Geometry
Equilibrium problem
Fixed points (mathematics)
Generalized projection
Lower semi-continuous
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Projection
Relatively non-expansive mapping
S. Park's Contribution to the Development of Fixed Point Theory and KKM Theory
Theorems
Topology
nonexpansive mapping
Relatively non-expansive mapping
Equilibrium problem
Lower semi-continuous
Generalized projection
Asymptotically quasi
Online AccessGet full text
ISSN1687-1812
1687-1820
1687-1812
DOI10.1186/1687-1812-2011-10

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Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi- ϕ -nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification : 47H05, 47H09, 47H10, 47J25
AbstractList Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi- ϕ -nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification : 47H05, 47H09, 47H10, 47J25
We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi--nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property.2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
ArticleNumber 10
Author Kim, Jong Kyu
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  fullname: Kim, Jong Kyu
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Cites_doi 10.4171/ZAA/1283
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ContentType Journal Article
Copyright Kim; 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: Kim; 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 nonexpansive mapping
Relatively non-expansive mapping
Equilibrium problem
Lower semi-continuous
Generalized projection
Asymptotically quasi
Language English
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Snippet We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi- ϕ -nonexpansive mapping and in the...
We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi--nonexpansive mapping and in the solution...
We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the...
Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in...
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SubjectTerms Analysis
Applications of Mathematics
Asymptotic properties
Asymptotically quasi-ϕ-nonexpansive mapping
Banach space
Classification
Convergence
Differential Geometry
Equilibrium problem
Fixed points (mathematics)
Generalized projection
Lower semi-continuous
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Projection
Relatively non-expansive mapping
S. Park's Contribution to the Development of Fixed Point Theory and KKM Theory
Theorems
Topology
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Title Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings
URI https://link.springer.com/article/10.1186/1687-1812-2011-10
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