Convergence theorems for uniformly quasi-φ-asymptotically nonexpansive mappings, generalized equilibrium problems, and variational inequalities
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Author list: Saewan S., Kumam P.
Publisher: SpringerOpen
Publication year: 2011
Journal: Journal of Inequalities and Applications (1025-5834)
Volume number: 2011
ISSN: 1025-5834
eISSN: 1029-242X
Languages: English-Great Britain (EN-GB)
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Abstract
In this article, we introduce an 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 variational inequality for an a-inverse-strongly monotone operator, and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results presented in this article improve and extend the recent results of Zegeye [Nonlinear Anal. 72, 2136-2146 (2010)], Wattanawitoon and Kumam [Nonlinear Anal. Hybrid Syst. 3(1), 11-20 (2009)] and many others. © 2011 Saewan and Kumam; licensee Springer.
Keywords
Iterative algorithms
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