A new class of generalized set-valued implicit variational inclusions in banach spaces with an application

Abstract

In this paper, we introduce and study a new class of generalized set-valued implicit variational inclusions in real Banach spaces. By using Nadler's Theorem and the resolvent operator technique for m-accretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this class of generalized set-valued implicit variational inclusions. We prove the existence of solution for this kind of generalized set-valued implicit variational inclusions without compactness and the convergence of iterative sequences generated by the algorithms in Banach spaces. We also give an application to generalized set-valued implicit variational inequalities in real Hilbert spaces.