The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems

In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ - asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α -inverse-str...

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Bibliographic Details
Published in:SpringerPlus Vol. 1; no. 1; pp. 8 - 14
Main Authors: Saewan, Siwaporn, Kumam, Poom
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2012
Springer Nature B.V
Springer International Publishing AG
Subjects:
Algorithms
Humanities and Social Sciences
Mathematics
multidisciplinary
Science
Science (multidisciplinary)
A system of equilibrium problem
47H10
Hybrid block iterative algorithm
Variational inequality
47H09
Inverse-strongly monotone operator
Uniformly quasi
asymptotically nonexpansive mapping
47H05
Uniformly quasi- ϕ-asymptotically nonexpansive mapping
ISSN:2193-1801, 2193-1801
Online Access:Get full text
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Summary:In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ - asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α -inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature.
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ISSN:2193-1801
2193-1801
DOI:10.1186/2193-1801-1-8