Implicit and explicit iterative algorithms for hierarchical variational inequality in uniformly smooth Banach spaces

Abstract

Abstract The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem. Our results improve and extend the corresponding results announced by some authors.

Keywords

• system of variational inequalities
• hierarchical variational inequality
• nonexpansive mapping
• fixed point
• implicit and explicit iterative algorithms
• global convergence