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An explicit iterative algorithm for a class of variational inequalities in Hilbert spaces. (English) Zbl 1251.47059
Let \(H\) be a Hilbert space and let \(F\) be a strongly monotone Lipschitz-continuous nonlinear operator \(F:H\to{H}\). The problem under consideration is to find a point \(p^\ast\in{C}\) such that \(\langle{F}(p^\ast),\,p=p^\ast\rangle\geq0\) for every \(p\in{C}\). Here, \(C\subset{H}\) is a closed convex set of common fixed points of a finite family of nonexpansive maps \(T_i:H\to{H}\), \(i=1,2,\dots,N\). The authors propose an explicit iterative procedure generating a sequence which strongly converges to the unique solution of the variational inequality.

MSC:
47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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