Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 40591, 14 pages
doi:10.1155/JIA/2006/40591

A new system of generalized nonlinear relaxed cocoercive variational inequalities

Ke Ding, Wen-Yong Yan, and Nan-Jing Huang

 Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
Received 21 November 2004; Revised 13 April 2005; Accepted 28 June 2005

Abstract

We introduce and study a new system of generalized nonlinear relaxed cocoercive inequality problems and construct an iterative algorithm for approximating the solutions of the system of generalized relaxed cocoercive variational inequalities in Hilbert spaces. We prove the existence of the solutions for the system of generalized relaxed cocoercive variational inequality problems and the convergence of iterative sequences generated by the algorithm. We also study the convergence and stability of a new perturbed iterative algorithm for approximating the solution.