International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 11, Pages 95723, 11 p.
doi:10.1155/IJMMS/2006/95723

Auxiliary principle for generalized nonlinear variational-like inequalities

Zeqing Liu1 , Haiyan Gao2 , Shin Min Kang3 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

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.