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  • Research Article
  • 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

  • Received: 25 September 2010
  • Accepted: 20 December 2010
  • Published:


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.


  • Variational Inequality
  • General System
  • Iteration Method
  • Common Element
  • Computational Biology

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Authors’ Affiliations

Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, China
Department of Business Administration, College of Management, Yuan-Ze University, Taoyuan Hsien, Chung-Li City, 330, Taiwan
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan


© 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.