On a Newton type iterative method for solving inclusions

We introduce a notion of strict differentiability for multifunctions by means of a notion of tangency based on a uniform property of Clarke's tangent cone. Given a multifunction G and a point (a, b) ∈G and assuming that the derivative DG(a, b) is surjective and has a bounded inverse, we build a sequence ((xn, yn)) ⊂ G, such that d(xn+1– xn, DG(a, b)⁻¹(–yn)) converges to 0. The sequence ((xn, yn)) is shown to converge to (x, 0) where x is a solution of 0∈G(x) provided the norm of ‖y0‖ is small enough. As a consequence we obtain an open mapping theorem for multifunctions whose proof is constructive.