New Wilker-type and Huygens-type inequalities

Year 2021, Volume: 50 Issue: 1, 46 - 62, 04.02.2021

Ling Zhu , Branko Malesevic

https://doi.org/10.15672/hujms.550184

Cited By: 1

Abstract

In this paper, we first determine the relationships between the first Wilker's inequality, the second Wilker's inequality, the first Huygens inequality, and the second Huygens inequality for circular functions and for hyperbolic functions, respectively. Then, we establish new Wilker-type inequalities and Huygens-type inequalities for two function pairs, $x/\sin^{-1}x$ and $x/\tan ^{-1}x$, $x/\sinh ^{-1}x$ and $x/\tanh ^{-1}x$. Finally, we obtain some more general conclusions than the first work of this paper, which reveal the absolute monotonicity of four functions involving the four inequalities mentioned above.

Keywords

Wilker-type inequalities, Huygens-type inequalities, circular functions, hyperbolic functions, inverse circular functions, inverse hyperbolic functions

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