Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 437976, 12 pages
doi:10.1155/2010/437976
Research Article

On the System of Nonlinear Mixed Implicit Equilibrium Problems in Hilbert Spaces

Yeol Je Cho1 and Narin Petrot2

1Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea
2Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 22 December 2009; Accepted 10 January 2010

Academic Editor: Jong Kyu Kim

Copyright © 2010 Yeol Je Cho and Narin Petrot. 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 use the Wiener-Hopf equations and the Yosida approximation notions to prove the existence theorem of a system of nonlinear mixed implicit equilibrium problems (SMIE) in Hilbert spaces. The algorithm for finding a solution of the problem (SMIE) is suggested; the convergence criteria and stability of the iterative algorithm are discussed. The results presented in this paper are more general and are viewed as an extension, refinement, and improvement of the previously known results in the literature.