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arXiv · 2009.01688

New Refinements of Cusa-Huygens inequality

Christophe Chesneau·Marko Kostic·Branko Malesevic·Bojan Banjac·Yogesh J. Bagul
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Abstract

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 $(2+\cos(x))/3 -(2/3-2/\pi)\Upsilon(x)$, where $\Upsilon(x) >0$ for $x\in (0, \pi/2)$, $\Upsilon(0)=0$ and $\Upsilon(\pi/2)=1$, such that $\sin x/x$ and the proposed bounds coincide at $x=0$ and $x=\pi/2$. The hierarchy of the obtained bounds is discussed, along with graphical study. Also, alternative proofs of the main result are given.

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Christophe Chesneau, Marko Kostic, Branko Malesevic, Bojan Banjac, Yogesh J. Bagul. 2020-09-01. New Refinements of Cusa-Huygens inequality. https://doi.org/10.1007/s00025-021-01392-8

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