Solution of a problem of S. Marcus concerning Jensen-convex functions

摘要

This paper is devoted to the problem of characterizing the class S of the stationary sets for J-convex functions Δ → R, where Δ is a convex open subset of R~n. We prove, among others, that a set T belongs to the class S if and only if T satisfies two conditions: the closure of the convex hull of T in the relative topology is the whole set Δ, and each J-convex function bounded above on T is continuous.