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Huang, Wangkang; Chen, Xiao-Diao; Chen, Linqiang; Mao, Xiaoyang

New inequalities for hyperbolic functions based on reparameterization. (English) Zbl 1454.26017

Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 115, No. 1, Paper No. 3, 16 p. (2021).
Some new inequalities involving hyperbolic functions with much better approximation effects are derived and proved. Specifically, the two sided bounds of \((\sinh(x)/x)^p\) for the case \(p\in(0,1]\) and the lower bound for the case \(p \geq 7/5\) are also established. In addition, mixed hyperbolic functions consisting of \(\tanh(x)\) and \(\sinh(x)\) are also considered. Numerical examples are provided to illustrate that the new inequalities obtained have better approximation effects than those of the previous results in the literature.
Reviewer: James Adedayo Oguntuase (Abeokuta)

Cited in 4 Documents

MSC:

26D05 Inequalities for trigonometric functions and polynomials
26D07 Inequalities involving other types of functions

Keywords:

inequalities; inverse tangent function; inverse hyperbolic sine function; inverse hyperbolic tangent function; sine function
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References:

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