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Journal of Mathematics
Volume 2013, Article ID 370143, 11 pages
http://dx.doi.org/10.1155/2013/370143
Research Article

Convergence of a Hybrid Iterative Scheme for Fixed Points of Nonexpansive Maps, Solutions of Equilibrium, and Variational Inequalities Problems

Department of Mathematical Sciences, Bayero University, P.M.B. 3011, Kano, Nigeria

Received 26 November 2012; Accepted 30 January 2013

Academic Editor: Liwei Zhang

Copyright © 2013 Bashir Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a closed, convex, and nonempty subset of a real -uniformly smooth Banach space , which is also uniformly convex. For some , let and be family of nonexpansive maps and -inverse strongly accretive map, respectively. Let be a bifunction satisfying some conditions. Let be a nonexpansive projection of onto . For some fixed real numbers , , and arbitrary but fixed vectors , let and be sequences generated by , , , , , where is fixed, and are sequences satisfying appropriate conditions. If , under some mild conditions, we prove that the sequences and converge strongly to some element in .