论文标题
Hermite-Hadamard不平等现象进行了重新审视：一些新的证明和申请
The Hermite-Hadamard inequality revisited: Some new proofs and applications
论文作者
论文摘要
提出了经典的Hermite-Hadamard不平等现象的新证据，并给出了几种应用，包括Hadamard类型的不等式的功能，其衍生物具有拐点或衍生物为凸的功能。此外，在功能的第一瞬间，某些估计值$％f：[a，b] \ rightarrow％tcimaCro {\ u {\ u {211d}}％％％beginexpansion \ mathbb {r}％end end Extexpansion ail central centment $ C =（a+b）/2 $ f：[0，\ infty）\ rightarrow（0，\ infty）$。
New proofs of the classical Hermite-Hadamard inequality are presented and several applications are given, including Hadamard-type inequalities for the functions, whose derivatives have inflection points or whose derivatives are convex. Morever, some estimates from below and above for the first moments of functions $% f:[a,b]\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion $ about the center point $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:[0,\infty )\rightarrow (0,\infty )$ is established.
