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Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings. (English) Zbl 1143.47047

The authors establish the strong convergence of an iteration scheme to a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a Lipschitz-continuous and monotone mapping in a real Hilbert space. The iteration scheme is based on the well-known hybrid and extragradient methods. They also introduce an iteration scheme that converges strongly to a common fixed point of two mappings, one of which is nonexpansive and the other is Lipschitz-continuous and pseudocontractive.

MSC:

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