Convergence theorems for mixed equilibrium problems, variational inequality problem and uniformly quasi-φ-asymptotically nonexpansive mappings
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Author list: Saewan S., Kumam P.
Publisher: Elsevier
Publication year: 2011
Journal: Applied Mathematics and Computation (0096-3003)
Volume number: 218
Issue number: 7
Start page: 3522
End page: 3538
Number of pages: 17
ISSN: 0096-3003
eISSN: 1873-5649
Languages: English-Great Britain (EN-GB)
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Abstract
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. © 2011 Elsevier Inc. All rights reserved.
Keywords
Uniformly quasi-φ- asymptotically nonexpansive mapping
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