A NEW SYSTEM OF GENERALIZED IMPLICIT SET-VALUED VARIATIONAL INCLUSIONS IN BANACH SPACES

Abstract

In this paper, we introduce and study a new system of generalized implicit set- valued variational inclusions involving generalized accretive operators in Banach spaces. By using the resolvent technique for the generalized accretive operator, we prove that this new system of generalized implicit set-valued variational inclusions is equivalent to a system of nonlinear operators equations. We give an algorithm for finding the solution of the new system of generalized implicit set-valued variational inclusions by employing the iterative method. Moreover, we show the existence of the solution of the new system of general- ized implicit set-valued variational inclusions and the convergence of the iterative sequences generated by the algorithm under some suitable assumptions.