Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 758786, 16 pages
doi:10.1155/2009/758786
Research Article

Auxiliary Principle for Generalized Strongly Nonlinear Mixed Variational-Like Inequalities

Zeqing Liu,1 Lin Chen,1 Jeong Sheok Ume,2 and Shin Min Kang3

1Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
2Department of Applied Mathematics, Changwon National University, Changwon 641-773, South Korea
3Department of Mathematics, Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, South Korea

Received 4 February 2009; Revised 24 April 2009; Accepted 27 April 2009

Academic Editor: Nikolaos Papageorgiou

Copyright © 2009 Zeqing Liu 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

We introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities, which includes several classes of variational inequalities and variational-like inequalities as special cases. By applying the auxiliary principle technique and KKM theory, we suggest an iterative algorithm for solving the generalized strongly nonlinear mixed variational-like inequality. The existence of solutions and convergence of sequence generated by the algorithm for the generalized strongly nonlinear mixed variational-like inequalities are obtained. The results presented in this paper extend and unify some known results.