Open Access

A new system of generalized nonlinear relaxed cocoercive variational inequalities

Journal of Inequalities and Applications20062006:40591

https://doi.org/10.1155/JIA/2006/40591

Received: 21 November 2004

Accepted: 28 June 2005

Published: 27 April 2006

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Sichuan University

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Copyright

© Ke Ding et al. 2006

This article is published under license to BioMed Central Ltd. 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.