Multivalued quasi-variational inclusions and multivalued accretive equations

Abstract

The purpose of this paper is to introduce and study a class of more general multivalued quasi-variational inclusions in Banach spaces. By using the accretive operator technique, we establish the equivalence between these kinds of multivalued quasi-variational inclusions and a kind of multivalued accretive equations in Banach space. Then, invoking Michael's selection theorem and Nadler's theorem, some existence theorems and iterative algorithms for solving this kind of multivalued quasi-variational inclusions in Banach spaces are established and suggested.