Set-valued quasi variational inclusions

Abstract

In this paper, we introduce and study a new class of variational inclusions, called the set-valued quasi variational inclusions. The resolvent operator technique is used to establish the equivalence between the set-valued quasi variational inclusions and the fixed point problem. This equivalence is used to study the existence of a solution and to suggest a number of iterative algorithms for solving the set-valued variational inclusions. We also study the convergence criteria of these algorithms.