Abstract: In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared in the considered problems, we have used the resolvent operator technique to suggest an iterative algorithm to compute approximate solutions of the system of nonlinear set valued variational inclusions. The convergence of the iterative sequences generated by algorithm is also proved.
Ams mathematics subject classification: 49J40; 47H06.
Keywords: Hilbert spaces; Iterative sequences; Lipschitz continuity; Resolvent operators; System of nonlinear set valued variational inclusions.