International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 95723, 11 pages
doi:10.1155/IJMMS/2006/95723

Auxiliary principle for generalized nonlinear variational-like inequalities

Zeqing Liu,1 Haiyan Gao,2 Shin Min Kang,3 and Soo Hak Shim4

1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian, Liaoning 116029, China
2Kingbridge Business College, Dongbei University of Finance and Economics, Dalian, Liaoning 116600, China
3Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, South Korea
4The Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, South Korea

Received 27 April 2005; Revised 23 March 2006; Accepted 25 April 2006

Copyright © 2006 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 new class of generalized nonlinear variational-like inequalities and prove an existence theorem of solutions for this kind of generalized nonlinear variational-like inequalities. By using the auxiliary principle technique, we construct a new iterative scheme for solving the class of the generalized nonlinear variational-like inequalities. The convergence of the sequence generated by the iterative algorithm is also discussed. Our results extend and unify the corresponding results due to Ding, Liu, Ume, Kang, Yao, and others.