On some set-valued iteration semigroups generated by interval-valued functions

Abstract

Let X be an arbitrary set.We characterize all interval-valued functions A : X → 2R for which a multifunction F : (0,∞)×X → 2X of the form F(t, x) = A− A(x)+min{t, q − inf A(x)} , where q = supA(X), is an iteration semigroup. The multifunction F is the set-valued counterpart of the fundamental form of continuous iteration semigroups of singlevalued functions on an interval.