# American Institute of Mathematical Sciences

February  2021, 20(2): 903-914. doi: 10.3934/cpaa.2020296

## Inequalities of Hermite-Hadamard type for higher order convex functions, revisited

 Intitute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

Received  July 2020 Revised  October 2020 Published  December 2020

In this paper we present a very short proof of inequalities of Hermite-Hadamard type obtained by M. Bessenyei and Zs. Páles. This proof is based on the recently developed method connected with use of stochastic orderings of random variables. In the second part of the paper we present a way to extend these known inequalities. Namely, we describe completely the possible inequalities of Hermite-Hadamard type for longer expression than it was the case in the results of Bessenyei and Páles.

Citation: Tomasz Szostok. Inequalities of Hermite-Hadamard type for higher order convex functions, revisited. Communications on Pure & Applied Analysis, 2021, 20 (2) : 903-914. doi: 10.3934/cpaa.2020296
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##### References:
The graphs of functions $F^{[1]}$ and $G^{[1]}$ in the case $2\alpha_1\geq x_2$
The graphs of functions $F^{[1]}$ and $G^{[1]}$ (with two crossing points in the interval $(x_2,x_3)$) in the case $2\alpha_1<x_2$
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