ON A FAMILY OF SET-VALUED FUNCTIONS

Let G be a linear continuous set-valued function defined on a closed convex cone C in a Banach space X. The aim of this paper is to show that for every x is an element of C and t greater than or equal to 0 a series B-t(x) = Sigma(i)(infinity)=(0)t(i)/i!G(i)(x) is convergent in the space of nonempty compact convex subsets of X with the Hausdorff metric. Moreover the inclusion(B-t o B-s)(x) subset of B-t+s(x) for x is an element of C and t, s greater than or equal to 0 holds true.