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

• 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.

Mathematics Subject Classification: Primary: 26A51, 26D10; Secondary: 39B62.

 Citation:

• Figure 1.  The graphs of functions $F^{[1]}$ and $G^{[1]}$ in the case $2\alpha_1\geq x_2$

Figure 2.  The graphs of functions $F^{[1]}$ and $G^{[1]}$ (with two crossing points in the interval $(x_2,x_3)$) in the case $2\alpha_1<x_2$

Figures(2)