Open Access

Finding Common Solutions of a Variational Inequality, a General System of Variational Inequalities, and a Fixed-Point Problem via a Hybrid Extragradient Method

Fixed Point Theory and Applications20102011:626159

https://doi.org/10.1155/2011/626159

Received: 25 September 2010

Accepted: 20 December 2010

Published: 29 December 2010

Abstract

We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-point set of a strictly pseudocontractive mapping in a real Hilbert space. Our hybrid method is based on the well-known extragradient method, viscosity approximation method, and Mann-type iteration method. By constrasting with other methods, our hybrid approach drops the requirement of boundedness for the domain in which various mappings are defined. Furthermore, under mild conditions imposed on the parameters we show that our algorithm generates iterates which converge strongly to a common element of these three problems.

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Authors’ Affiliations

(1)
Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities
(2)
Department of Business Administration, College of Management, Yuan-Ze University
(3)
Department of Applied Mathematics, National Sun Yat-sen University

Copyright

© Lu-Chuan Ceng et al. 2011

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.