Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 134148, 17 pages
An Extragradient Approximation Method for Equilibrium Problems and Fixed Point Problems of a Countable Family of Nonexpansive Mappings
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Received 28 February 2008; Accepted 13 July 2008
Academic Editor: Huang Nanjing
Copyright © 2008 Rabian Wangkeeree. 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.
We introduce a new iterative scheme for finding the common element of the set of common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the
variational inequality. We show that the sequence converges strongly to a common element of the above three sets under
some parameters controlling conditions. Moreover, we apply our result to the problem of finding a common fixed point
of a countable family of nonexpansive mappings, and the problem of finding a zero of a monotone operator. This main
theorem extends a recent result of Yao et al. (2007) and many others.