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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 131890, 23 pages
http://dx.doi.org/10.1155/2011/131890
Research Article

A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems

1Mathematics Institute, African University of Science and Technology, Abuja, Nigeria
2Department of Mathematics, University of Nigeria, Nsukka, Nigeria

Received 14 February 2011; Accepted 14 April 2011

Academic Editor: Yonghong Yao

Copyright © 2011 Yekini Shehu. 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

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized -projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.