Advances in Operations Research
Volume 2012 (2012), Article ID 843486, 18 pages
http://dx.doi.org/10.1155/2012/843486
Research Article

On a System of Generalized Mixed Equilibrium Problems Involving Variational-Like Inequalities in Banach Spaces: Existence and Algorithmic Aspects

H. Mahdioui1 and O. Chadli2

1Department of Mathematics, Ibnou Zohr University, Agadir 80000, Morocco
2Department of Economics, Ibnou Zohr University, B.P. 8658 Poste Dakhla, Agadir 80000, Morocco

Received 28 January 2012; Accepted 15 June 2012

Academic Editor: Abdellah Bnouhachem

Copyright © 2012 H. Mahdioui and O. Chadli. 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 study the existence and the algorithmic aspect of a System of Generalized Mixed Equilibrium Problems involving variational-like inequalities (SGMEPs) in the setting of Banach spaces. The approach adopted is based on the auxiliary principle technique and arguments from generalized convexity. A new existence theorem for the auxiliary problem is established; this leads us to generate an algorithm which converges strongly to a solution of (SGMEP) under weaker assumptions. When the study is reduced to the setting of reflexive Banach spaces, then it can be more relaxed by dropping the coercivity condition. The results obtained in this paper are new and improve some recent studies in this field.