Weak and strong convergence of hybrid subgradient method for pseudomonotone equilibrium problem and multivalued nonexpansive mappings

In this paper, we introduce a hybrid subgradient method for finding a common element of the set of solutions of a class of pseudomonotone equilibrium problems and the set of fixed points of a finite family of multivalued nonexpansive mappings in Hilbert space. The proposed method involves only one p...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering 2014-11, Vol.2014 (1), p.1-14, Article 232
Main Author: Wen, Dao-Jun
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Convergence
Differential Geometry
Hilbert space
Iterative methods
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Projection
Topology
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Summary:In this paper, we introduce a hybrid subgradient method for finding a common element of the set of solutions of a class of pseudomonotone equilibrium problems and the set of fixed points of a finite family of multivalued nonexpansive mappings in Hilbert space. The proposed method involves only one projection rather than two as in the existing extragradient method and the inexact subgradient method for an equilibrium problem. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. Moreover, a numerical example is given to illustrate our algorithm and our results. MSC: 47H05, 47H09, 47H10.
ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/1687-1812-2014-232