Abstract and Applied Analysis
Volume 2010 (2010), Article ID 861031, 24 pages
doi:10.1155/2010/861031
Research Article

A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems

Yekini Shehu1,2

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

Received 21 September 2010; Revised 9 November 2010; Accepted 22 December 2010

Academic Editor: A. Zafer

Copyright © 2010 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 weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth using the properties of generalized 𝑓 -projection operator. Using this result, we discuss strong convergence theorem concerning general 𝐻 -monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.