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Acta Applicandae Mathematicae

, Volume 110, Issue 3, pp 1211–1224 | Cite as

Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces

  • Yonghong Yao
  • Muhammad Aslam NoorEmail author
  • Khalida Inayat Noor
  • Yeong-Cheng Liou
  • Huma Yaqoob
Article

Abstract

In this paper, we introduce a new system of general variational inequalities in Banach spaces. We establish the equivalence between this system of variational inequalities and fixed point problems involving the nonexpansive mapping. This alternative equivalent formulation is used to suggest and analyze a modified extragradient method for solving the system of general variational inequalities. Using the demi-closedness principle for nonexpansive mappings, we prove the strong convergence of the proposed iterative method under some suitable conditions.

Keywords

Variational inequality Iterative method Nonexpansive mapping Fixed point 

Mathematics Subject Classification (2000)

47H05 47H10 47J25 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Yonghong Yao
    • 1
  • Muhammad Aslam Noor
    • 2
    Email author
  • Khalida Inayat Noor
    • 2
  • Yeong-Cheng Liou
    • 3
  • Huma Yaqoob
    • 2
  1. 1.Department of MathematicsTianjin Polytechnic UniversityTianjinChina
  2. 2.Mathematics DepartmentCOMSATS Institute of Information TechnologyIslamabadPakistan
  3. 3.Department of Information ManagementCheng Shiu UniversityKaohsiungTaiwan

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