$n$-convexity and majorization
Josip E. Pečarić, D. Zwick · Rocky Mountain Journal of Mathematics · 1989
The fact that the n th order divided difference of an (n + 2)-convex function is a symmetric, convex function of its arguments, and is therefore Schur convex, allows us to apply the theory of Majorization in order to derive inequalities for such functions.Several consequences of this result are presented.In a separate section the theory of majorization is used to compute bounds on the derivatives of polynomials.