Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 20457, 6 pages
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

Academic Editor: Yeol Je Cho

Copyright © 2007 Xiaolong Qin and Meijuan Shang. 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 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.