This paper describes and presents a method for finding the zero of the sum of two monotone operators on real Hilbert spaces. In addition, some illustrative examples are given at the end of this paper.
The aim of this paper is to calculate the approximate solution of differential inclusion with prox-regular set, the question is how to calculate this solution? We use the discrete approximation property of a new variant of nonconvex sweeping processes involving normal cone and a finite element method. Knowing that the majority of mathematicians have proved only the existence and uniqueness of the solution for this type of inclusions, like: Mordukhovich, Thibault, Aubin, Messaoud,...etc.
MSC Classification: 34A60 , 49J52 , 37B25.
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