Sandwich Theorems for Operators of Convex Type

This note centers around a class of operators from a real vector space into a Dedekind complete ordered real vector space, which satisfy the usual convexity inequalities only with respect to some given subset Λ of the unit interval. It is shown that between a Λ-concave and a Λ-convex operator one can always find a Λ-affine operator. Several applications of this sandwich principle are given.