On Wright- but not Jensen-convex functions
of higher order

Abstract. In this paper, we construct a general class of real functions whose members, for odd
\(n\), are \(n\)th-order Jensen-convex but not \(n\)th-order Wright-convex. This implies, for odd \(n\), that the class of \(n\)th-order Jensen-convex functions is strictly bigger than that of \(n\)th-order Wright-convex functions while the analogous problem for even \(n\) remains unsolved.