Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 64947, 10 pages
doi:10.1155/2007/64947
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

Recommended by Simeon Reich

Abstract

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.