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An extragradient-like approximation method for variational inequality problems and fixed point problems. (English) Zbl 1124.65056
Summary: The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. The authors introduce an extragradient-like approximation method based on the so-called extragradient method and a viscosity approximation method. A strong convergence theorem is proved for two iterative sequences generated by this method.
MSC:
65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
47H10Fixed point theorems for nonlinear operators on topological linear spaces
49M25Discrete approximations in calculus of variations
47H09Mappings defined by “shrinking” properties