New viscosity method for hierarchical fixed point approach to variational inequalities
Wei-Qi Deng · Fixed Point Theory and Applications · 2013
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.