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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Vydáno v:Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2018; číslo 1; s. 1 - 17
Hlavní autoři: Phuengrattana, Withun, Lerkchaiyaphum, Kritsada
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.03.2018
SpringerOpen
Témata:
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
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Popis
Shrnutí: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