Abstract and Applied Analysis
Volume 2011 (2011), Article ID 632857, 22 pages
http://dx.doi.org/10.1155/2011/632857
Research Article

A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems

Utith Inprasit and Weerayuth Nilsrakoo

Department of Mathematics, Statistics, and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand

Received 17 March 2011; Revised 3 June 2011; Accepted 13 June 2011

Academic Editor: Norimichi Hirano

Copyright © 2011 Utith Inprasit and Weerayuth Nilsrakoo. 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

A new modified Halpern-Mann type iterative method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. The results presented in this work improve on the corresponding ones announced by many others.