International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1843-1851
doi:10.1155/IJMMS.2005.1843
Existence and algorithm of solutions for generalized nonlinear variational-like inequalities
Zeqing Liu1
, Juhe Sun1
, Soo Hak Shim3
and Shin Min Kang3
1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Liaoning, Dalian 116029, China
3Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, Korea
Abstract
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.