论文标题
Cusa-Huygens不平等的新细化
New Refinements of Cusa-Huygens inequality
论文作者
论文摘要
在论文中，我们通过简单的功能来完善和扩展Cusa-Huygens的不等式。特别是，我们确定$ \ sin（x）/x $的急剧界限$（2+ \ cos（x））/3 - （2/3-2/π） $ x = 0 $和$ x =π/2 $重合。与图形研究一起讨论了获得的边界的层次结构。另外，给出了主要结果的替代证明。
In the paper, we refine and extend Cusa-Huygens inequality by simple functions. In particular, we determine sharp bounds for $\sin(x) /x$ of the form $(2+\cos(x))/3 -(2/3-2/π)Υ(x)$, where $Υ(x) >0$ for $x\in (0, π/2)$, $Υ(0)=0$ and $Υ(π/2)=1$, such that $\sin x/x$ and the proposed bounds coincide at $x=0$ and $x=π/2$. The hierarchy of the obtained bounds is discussed, along with graphical study. Also, alternative proofs of the main result are given.
