Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces
Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces
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DOI：
10.1007/s10440-009-9502-9
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发表时间：
2010-06
影响因子：
1.6
通讯作者：
Yonghong Yao;Muhammad Aslam Noor-Muhammad-Aslam Noor-147407199;Khalida Inayat Noor-Khalida-Inayat Noor-147215883;Y. Liou;Humaira Yaqoob
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文献类型：
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作者：
Yonghong Yao;Muhammad Aslam Noor-Muhammad-Aslam Noor-147407199;Khalida Inayat Noor-Khalida-Inayat Noor-147215883;Y. Liou;Humaira Yaqoob
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.
