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  • Research Article
  • Open Access

Algorithms Construction for Variational Inequalities

Fixed Point Theory and Applications20112011:794203

  • Received: 4 October 2010
  • Accepted: 19 February 2011
  • Published:


We devote this paper to solving the variational inequality of finding with property such that for all . Note that this hierarchical problem is associated with some convex programming problems. For solving the above VI, we suggest two algorithms: Implicit Algorithmml: for all and Explicit Algorithm: for all . It is shown that these two algorithms converge strongly to the unique solution of the above VI. As special cases, we prove that the proposed algorithms strongly converge to the minimum norm fixed point of .


  • Variational Inequality
  • Differential Geometry
  • Computational Biology
  • Full Article
  • Algorithm Construction

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Authors’ Affiliations

Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China
Department of Information Management, Cheng Shiu University, Kaohsiung, 833, Taiwan
Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Republic of Korea


© Yonghong Yao 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.