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 map**. 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 map**s, we prove the strong convergence of the proposed iterative method under some suitable conditions.
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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