Regularization and iterative method for general variational inequality problem in hilbert spaces
1 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea
2 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Journal of Inequalities and Applications 2011, 2011:21 doi:10.1186/1029-242X-2011-21Published: 20 July 2011
Without the strong monotonicity assumption of the mapping, we provide a regularization method for general variational inequality problem, when its solution set is related to a solution set of an inverse strongly monotone mapping. Consequently, an iterative algorithm for finding such a solution is constructed, and convergent theorem of the such algorithm is proved. It is worth pointing out that, since we do not assume strong monotonicity of general variational inequality problem, our results improve and extend some well-known results in the literature.