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
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
Received 21 November 2004; Revised 13 April 2005; Accepted 28 June 2005
Copyright © 2006 Ke Ding 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.
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.