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Modified extragradient methods for a system of variational inequalities in Banach spaces. (English) Zbl 1192.47065
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.

MSC:
47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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