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arXiv · 2008.06280

Hermite-Hadamard inequalities for (p,a,b)-convex functions

Bar Light
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Abstract

A function $f:[a,b] \rightarrow \mathbb{R}$ is called $(p,a,b)$-convex if $f$ is $p$ times continuously differentiable, $f^{(p)}$ is convex and increasing, and $f^{(k)}(a)=0$ for all $k=1,\ldots,p$ where $f^{(j)}$ is the $j$th derivative of $f$. In this note we prove Hermite-Hadamard inequalities for $(p,a,b)$-convex functions that are significantly tighter than the classical Hermite-Hadamard inequality. We also prove inequalities for fractional integrals that involve $(p,a,b)$-convex functions.

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Bar Light. 2020-08-14. Hermite-Hadamard inequalities for (p,a,b)-convex functions. https://arxiv.org/abs/2008.06280

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