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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.
47J25Iterative procedures (nonlinear operator equations)
47J20Inequalities involving nonlinear operators
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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