Semigroups of Jensen set-valued functions

A set-valued function F defined on a convex cone S in a real vector space X into the set n(Y) of all non-empty subsets of a real vector space Y is said to be the Jensen function iff $${1\over 2}\lbrack F(x)+F(x)\rbrack=F\lbrack{1\over 2}(x+y)\rbrack$$ for all x, y ∈ S. This note deals with iteration semigroups of Jensen set-valued functions on S.