We consider a variational optimization problem involving multifunctions and we prove a stability result with respect to the Monge-Kantorovich metric. We then show an application to variational problems defined on fractals generated by Iterated Function Systems.

In this paper we establish under suitable conditions the existence of measurable selectors for Gs-valued multifunctions. In particular we prove that a measurable partition of a Polish space into G6 sets admits a Borel selector.

We present a new inverse mapping theorem for correspondences. It uses a notion of differentiability for multifunctions which seems to be new. We compare it with previous versions. We provide an application to differential inclusions.

Let F be a multifunction with values in Lp(Ω, X). In this note, we study which regularity properties of F are preserved when we consider the decomposable hull of F .

In this present paper, we introduce and investigate a new form of mappings namely; upper lower M-asymmetric preirresolute multifunctions defined between M-structural asymmetric topological spaces. The relationships the in our sense other types precountinuous on both symmetric structures are discussed.

For a Banach space X we demonstrate the equivalence of following two properties: (1) is B-convex (that is, possesses nontrivial infratype), and (2) if F:[0,1]→2X∖{∅} multifunction with bounded values, convF denotes t↦conv(F(t)), then Riemann integrability equivalent to F. multifunctions relatively norm compact values F without any restrictions on X.