On increasing iteration semigroup of Jensen set-valued functions (Q2662892)

Let \(cc(Y)\) denote the family of all nonempty, compact and convex subsets of a Hausdorff topological vector space \(Y\). Let \(F : K \to cc(Y)\) be a Jensen set-valued function for a convex cone \(K\) in a vector space \(X\). The author proves the existence of the unique additive set-valued function \(A : K \to cc(Y )\) and a unique constant set \(B \in cc(Y )\) for which \(F(x) = A(x) + B\) where \(x \in K\).