Hybrid viscosity approximation methods for systems of variational inequalities and hierarchical fixed point problems

Abstract

In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities (GSVI) with a hierarchical fixed point problem (HFPP) constraint
for an infinite family of nonexpansive mappings. We show that under appropriate
conditions the proposed algorithms converge strongly to a solution of the GSVI, which is also a unique solution of the HFPP.