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Abstract and Applied Analysis
Volume 2013, Article ID 737590, 19 pages
http://dx.doi.org/10.1155/2013/737590
Research Article

A New Hybrid Extragradient Iterative Method for Approximating the Common Solutions of a System of Variational Inequalities, a Mixed Equilibrium Problem, and a Hierarchical Fixed Point Problem

1School of Management Science and Engineering, Nanjing University, Nanjing 210093, China
2Ibn Zohr University, ENSA, BP 1136, Agadir, Morocco
3Department of Mathematics, Statistics and Physics College of Arts and Sciences, Qatar University, P.O. Box 2713, Doha, Qatar

Received 31 August 2013; Accepted 4 October 2013

Academic Editor: Erdal Karapınar

Copyright © 2013 Abdellah Bnouhachem and Abdelouahed Hamdi. 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 suggest and analyze an iterative scheme for finding the approximate element of the common set of solutions of a system of variational inequalities, a mixed equilibrium problem, and a hierarchical fixed point problem in a real Hilbert space. Strong convergence of the proposed method is proved under some conditions. The results presented in this paper extend and improve some well-known results in the literature.