The characterization of some set-valued iteration semigroups (Q2350279)

Let \(X\) be a set. A multifunction \(F: (0,\infty) \times X \to2^X\) is said to be a set-valued iteration semigroup if \(F(t+s,x) = F(t,F(s,x))\) for \(x \in X\) and \(s, t \in (0,\infty)\). The author gives a characterization of set-valued iteration semigroups which are the counterparts of the fundamental form of continuous iteration semigroups of single-valued functions on an interval; see also [\textit{G. Łydzińska}, Publ. Math. 64, No. 3--4, 285--298 (2004; Zbl 1071.39023)].