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

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China

    Yonghong Yao

  2. Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

    Muhammad Aslam Noor, Khalida Inayat Noor & Huma Yaqoob

  3. Department of Information Management, Cheng Shiu University, Kaohsiung, 833, Taiwan

    Yeong-Cheng Liou

Authors
  1. Yonghong Yao
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  2. Muhammad Aslam Noor
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  3. Khalida Inayat Noor
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  4. Yeong-Cheng Liou
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  5. Huma Yaqoob
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Corresponding author

Correspondence to Muhammad Aslam Noor.

Additional information

The fourth author was partially supposed by the Grant NSC 97-2221-E-230-017.

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Yao, Y., Aslam Noor, M., Inayat Noor, K. et al. Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces. Acta Appl Math 110, 1211–1224 (2010). https://doi.org/10.1007/s10440-009-9502-9

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  • DOI: https://doi.org/10.1007/s10440-009-9502-9

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