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

Abstract

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 f is strongly Wright-convex of order n if and only if it is of the form f(x) = g(x)+p(x)+cx n+1 , 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.