Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 64947, 10 pages
Research Article

Wiener-Hopf Equations Technique for General Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Yongfu Su,1 Meijuan Shang,1,2 and Xiaolong Qin3

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China
3Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

Received 1 July 2007; Accepted 3 October 2007

Academic Editor: Simeon Reich

Copyright © 2007 Yongfu Su 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 show that the general variational inequalities are equivalent to the general Wiener-Hopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality involving multivalued relaxed monotone operators. Our results improve and extend recent ones announced by many others.