On the Ra?a Inequality for Higher Order Convex Functions

Abstract We study the following $$(q-1)$$ ( q - 1 ) th convex ordering relation for q convolution power of difference probability distributions $$\mu $$ ? and $$\nu ? $$\begin{aligned} (\nu -\mu )^{*q}\ge _{(q-1)cx} 0 , \quad q\ge 2, \end{aligned}$$ ? ? c x 0 , 2 we obtain theorem providing a useful sufficient condition its verification. apply this various families several inequalities related to classical interpolation operators. In particular, taking binomial distributions, new, very short proof inequality given recently by Abel Leviatan (2020).