Journal of Applied Mathematics
Volume 2012 (2012), Article ID 690648, 18 pages
http://dx.doi.org/10.1155/2012/690648
Research Article

Projection Methods and a New System of Extended General Regularized Nonconvex Set-Valued Variational Inequalities

Javad Balooee,1 Yeol Je Cho,2 and Mee Kwang Kang3

1Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran
2Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
3Department of Mathematics, Dongeui University, Pusan 614–714, Republic of Korea

Received 2 October 2011; Accepted 11 November 2011

Academic Editor: Rudong Chen

Copyright © 2012 Javad Balooee et al. 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 system of extended general nonlinear regularized nonconvex set-valued variational inequalities is introduced, and the equivalence between the extended general nonlinear regularized nonconvex set-valued variational inequalities and the fixed point problems is verified. Then, by this equivalent formulation, a new perturbed projection iterative algorithm with mixed errors for finding a solution of the aforementioned system is suggested and analyzed. Also the convergence of the suggested iterative algorithm under some suitable conditions is proved.