论文标题
HERMITE-HADAMARD不平等现象（P，a，b） - 凸函数
Hermite-Hadamard inequalities for (p,a,b)-convex functions
论文作者
论文摘要
a函数$ f：[a，b] \ rightarrow \ mathbb {r} $称为$（p，a，a，b）$ - 如果$ f $是$ f $ as $ p $ times连续可区分，$ f^{（p）} $是convex and convex and naving and nabling and naving and ungning and $ f^{（k）}（k）}（a）= 0 $ for $ k for ld $ k = 1， $ f^{（j）} $是$ f $的$ j $ th导数。在本说明中，我们证明了hermite-hadamard的不平等现象（p，a，b）$ - 凸功能，其功能比经典的hermite-hadamard不平等明显更紧。我们还证明了涉及$（p，a，b）$ - 凸功能的分数积分的不等式。
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.
