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Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces. (English) Zbl 1147.65048
The authors introduce a new iterative method to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. No numerical tests are presented.
MSC:
65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
65J15Equations with nonlinear operators (numerical methods)
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
49M20Methods of relaxation type in calculus of variations