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 \(\tilde{x}\in H\); \(\tilde{x}=(\mathrm{proj}_{F(t)}S)\tilde{x}\), where \(H\) is a Hilbert space, \(S\) is some nonlinear operator and \(T\) is a nonexpansive mapping on a closed convex subset \(C\) and \(\mathrm{proj}_{F(t)}\) 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.


65J15 Numerical solutions to equations with nonlinear operators
65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
Full Text: DOI


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