On solving the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings

We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered pro...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2018; no. 1; pp. 1 - 17
Main Authors: Phuengrattana, Withun, Lerkchaiyaphum, Kritsada
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2018
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Differential Geometry
Fixed point problems
Hilbert spaces
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Nonexpansive multivalued mapping
Split generalized equilibrium problems
Topology
47H10
65K15
Nonexpansive multivalued mapping
47H09
Hilbert spaces
65K10
Fixed point problems
Split generalized equilibrium problems
ISSN:1687-1812, 1687-1812
Online Access:Get full text
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Summary:We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-018-0631-6