Convergence theorems for mixed equilibrium problems, variational inequality problem and uniformly quasi- ϕ-asymptotically nonexpansive mappings

We introduce a modified block hybrid projection 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 variational inequality for an α-inverse-strongly monotone operator, the...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 218; no. 7; pp. 3522 - 3538
Main Authors: Saewan, Siwaporn, Kumam, Poom
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2011
Subjects:
Banach space
Blocking
Convergence
Inequalities
Inverse-strongly monotone operator
Mapping
Mathematical models
Mixed equilibrium problem
Modified block iterative algorithm
Projection
Theorems
Uniformly quasi- ϕ-asymptotically nonexpansive mapping
Variational inequality
Modified block iterative algorithm
Uniformly quasi- ϕ-asymptotically nonexpansive mapping
Inverse-strongly monotone operator
Mixed equilibrium problem
Variational inequality
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:We introduce a modified block hybrid projection 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 variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problems. Then, we obtain strong convergence theorems for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.08.099