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Strong convergence of an iterative method for variational inequality problems and fixed point problems. (English) Zbl 1210.47097
Summary: In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximation methods. Strong convergence theorems are established in a real Hilbert space.

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.
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