Open Access

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

Fixed Point Theory and Applications20082008:634921

DOI: 10.1155/2008/634921

Received: 23 October 2007

Accepted: 25 January 2008

Published: 25 February 2008

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Liaoning Normal University
(2)
Department of Mathematics and the Research Institute of Natural Science, Gyeongsang National University
(3)
Department of Applied Mathematics, Changwon National University

Copyright

© Zeqing Liu et al. 2008

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.