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On additive correspondences

Aghajani M., Smajdor A.

Journal of Applied Analysis

2015

Vol. 21, nr 1

59--61

The existence of additive selections of additive correspondences was investigated in [3, 4, 6] and other papers. In this article, we find an existence theorem for additive selections of additive correspondences with convex compact values in a real normed linear space defined on an open convex cone of a real separable normed space.

Hukuhara`s derivative and concave iteration semigroups of linear set-valued functions

Smajdor A.

Journal of Applied Analysis

2002

Vol. 8, nr 2

297-305

Let K be a closed convex cone with the nonempty interior in a real Banach space and cc(K) denote the family of all nonempty convex compact subsets of K. If {Ff : t ≥ 0} is a concave iteration semigroup of continuous linear set-valued functions Ft : K → cc(K) with F°(x) = {x} for x ∈ K, then DtFt(x) = Ft (G(x)) for x ∈ K and t ≥ 0, where DtFt(x) denotes the Hukuhara derivative of Ft(x) with respect to t and (wzór) for x ∈ K.