Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 20457, 6 pages
doi:10.1155/2007/20457
Research Article

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Xiaolong Qin1 and Meijuan Shang2

 1Department of Mathematics and the RINS, Gyeongsang National University, Chinju 660701, South Korea
2Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China
Received 31 July 2007; Accepted 3 December 2007

Recommended by Yeol Je Cho

Abstract

We consider the solvability of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued nonexpansive mappings in the framework of Hilbert spaces. We also study the convergence criteria of iterative methods under some mild conditions. Our results improve and extend the recent ones announced by many others.