Abstract
A new viscosity method for hierarchically approximating some common fixed point of an infinite family of nonexpansive mappings is presented; and some strong convergence theorems for solving variational inequality problems and hierarchical fixed point problems are obtained without the aid of the convex linear combination of a countable family of nonexpansive mappings. Solutions are sought in the set of fixed points of another nonexpansive mapping. The results improve those of the authors with the related interest.MSC:47H09, 47H10, 65J15, 47J25.
Highlights
Introduction and preliminariesA fairly common method in solving some nonlinear problems is to replace the original problems by a family of regularized ones
Let {Tn} : H → H be a countable family of nonexpansive mappings with F :=
The existence problem of hierarchical fixed points for a single nonexpansive mapping and approximation problem in the setting of Hilbert spaces has been studied by several authors
Summary
Introduction and preliminariesA fairly common method in solving some nonlinear problems is to replace the original problems by a family of regularized (or perturbed) ones. Let {Tn} : H → H be a countable family of nonexpansive mappings with F :=
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