Characterizations and decomposition of strongly wright-convex functions of higher order

Motivated by results on strongly convex and strongly Jensen-convex functions by R. Ger and K. Nikodem in [Strongly convex functions of higher order, Nonlinear Anal. 74 (2011), 661-665] we investigate strongly Wright-convex functions of higher order and we prove decomposition and characterization theorems for them. Our decomposition theorem states that a function / is strongly Wright-convex of order n if and only if it is of the form [formula], where g is a (continuous) n-convex function and p is a polynomial function of degree n. This is a counterpart of Ng's decomposition theorem for Wright-convex functions. We also characterize higher order strongly Wright-convex functions via generalized derivatives.