Systems of variational inequalities with hierarchical variational inequality constraints in Banach spaces

摘要

Two implicit iterative algorithms are presented to solve a general system of variational inequalities with the hierarchical variational inequality constraint for an infinite family of nonexpansive mappings. Strong convergence theorems are given in a uniformly convex and 2-uniformly smooth Banach space. The results improve and extend the corresponding results in the earlier and recent literature.