Open Access Research Article

The Solvability of a Class of General Nonlinear Implicit Variational Inequalities Based on Perturbed Three-Step Iterative Processes with Errors

Zeqing Liu1, ShinMin Kang2* and JeongSheok Ume3

Author Affiliations

1 Department of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian, Liaoning 116029, China

2 Department of Mathematics and the Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, South Korea

3 Department of Applied Mathematics, Changwon National University, Changwon 641-733, South Korea

For all author emails, please log on.

Fixed Point Theory and Applications 2008, 2008:634921  doi:10.1155/2008/634921


The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2008/1/634921


Received: 23 October 2007
Accepted: 25 January 2008
Published: 25 February 2008

© 2008 The Author(s).

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 class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem, we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several existence and uniqueness results of solutions for the general nonlinear implicit variational inequalities, and convergence and stability results of the sequence generated by the algorithm are obtained. The results presented in this paper extend, improve, and unify a host of results in recent literatures.

Publisher note

To access the full article, please see PDF.