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Zbl 1192.47065
Yao, Yonghong; Aslam Noor, Muhammad; Inayat Noor, Khalida; Liou, Yeong-Cheng; Yaqoob, Huma
(Yao, Yong-hong)
Modified extragradient methods for a system of variational inequalities in Banach spaces. (English)
[J] Acta Appl. Math. 110, No. 3, 1211-1224 (2010). ISSN 0167-8019; ISSN 1572-9036/e

The authors establish the equivalence of a system of variational inequalities to a fixed point problem. This equivalence is employed to construct an iterative method for which the strong convergence to the solution is proven.
[Dumitru Motreanu (Perpignan)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47J20 Inequalities involving nonlinear operators
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: variational inequality; iterative method; nonexpansive mapping; fixed point

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Zentralblatt MATH Berlin [Germany]