Semigroups of Jensen set-valued functions (Q1895206)

Let \(S\) be a closed convex cone in a normed space \(X\) and \(cc(S)\) be the family of all compact convex non-empty subsets of \(S\). It is proved that (under suitable assumptions) the family of set-valued functions \(F^t: S\to cc(S)\), \(t\geq 0\), is an increasing iteration semigroup of Jensen functions iff there exist an additive function \(f: X\to X\) and sets \(B, C\in cc(S)\) such that \(F^t(x)= f(x)+ tC+ B\), \(t\geq 0\), \(x\in S\).