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Chen, Chao-Ping; Cheung, Wing-Sum

Wilker- and Huygens-type inequalities and solution to Oppenheim’s problem. (English) Zbl 1254.26022

Integral Transforms Spec. Funct. 23, No. 5, 325-336 (2012).
The main result of this paper is a pair of inequalities involving only first year calculus: For every \(x\in(-1,0)\cup(0,1)\) it is true that \(\left( x/\arcsin x\right) ^{2}+x/\arctan x<2\) and \(\left( x/\text{arsinh} x\right) ^{2}+x/\text{artanh}x<2.\)
Reviewer: Constantin Niculescu (Craiova)

Cited in 17 Documents

MSC:

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

Keywords:

Wilker inequality; Huygens inequality; inverse trigonometric functions; inverse hyperbolic functions
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References:

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