Concave itération semigroups of Jensen set-valued functions

Abstract

Let S be a closed convex cone such that int S ≠ 0 in a real separable Banach space. A necessary and sufficient condition is given under which a family {F[t] : t ≥ 0} of set-valued functions F[t] : S -> cc(S) is a concave iteration semigroup of continuous Jensen set- valued functions.