On the hierarchical variational inclusion problems in Hilbert spaces

Abstract

Abstract The purpose of this paper is by using Maingé’s approach to study the existence and approximation problem of solutions for a class of hierarchical variational inclusion problems in the setting of Hilbert spaces. As applications, we solve the convex programming problems and quadratic minimization problems by using the main theorems. Our results extend and improve the corresponding recent results announced by many authors. MSC: 47J05, 47H09, 49J25.