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Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method. (English) Zbl 1197.49008
Summary: In this paper, we introduce an iterative method based on the extragradient method for finding a common element of the set of a general system of variational inequalities and the set of fixed points of a strictly pseudocontractive mapping in a real Hilbert space. Furthermore, we prove that the studied iterative method strongly converges to a common element of the set of a general system of variational inequalities and the set of fixed points of a strictly pseudocontractive mapping under some mild conditions imposed on algorithm parameters.

MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47N10Applications of operator theory in optimization, convex analysis, programming, economics
65J15Equations with nonlinear operators (numerical methods)
65K15Numerical methods for variational inequalities and related problems
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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