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Iterative algorithms for hierarchical fixed points problems and variational inequalities. (English) Zbl 1205.65192
Summary: This paper deals with a method for approximating a solution of the fixed point problem: find x ˜H; x ˜=( proj F(t) S)x ˜, where H is a Hilbert space, S is some nonlinear operator and T is a nonexpansive mapping on a closed convex subset C and proj F(t) denotes the metric projection on the set of fixed points of T. First, we prove a strong convergence theorem by using a projection method which solves some variational inequality. As a special case, this projection method also solves some minimization problems. Secondly, under different restrictions on parameters, we obtain another strong convergence result which solves the above fixed point problem.

MSC:
65J15Equations with nonlinear operators (numerical methods)
65K15Numerical methods for variational inequalities and related problems
49J40Variational methods including variational inequalities
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