International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1843-1851

Existence and algorithm of solutions for generalized nonlinear variational-like inequalities

Zeqing Liu,1 Juhe Sun,1 Soo Hak Shim,2 and Shin Min Kang2

1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Liaoning, Dalian 116029, China
2Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, Korea

Received 28 December 2004; Revised 9 June 2005

Copyright © 2005 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.


We introduce and study a new class of generalized nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of generalized nonlinear variational-like inequalities. A new iterative algorithm for finding the approximate solutions of the generalized nonlinear variational-like inequality is given and the convergence of the algorithm is also proved. The results presented in this paper improve and generalize some results in recent literature.