New inequalities of Huygens-type involving tangent and sine functions

Year 2023, Volume: 52 Issue: 1, 36 - 61, 15.02.2023

Ling Zhu , Branko Malesevic

https://doi.org/10.15672/hujms.951700

Cited By: 1

https://izlik.org/JA67CU46CU

Abstract

Using the estimations of the even-indexed Bernoulli number and Euler number this paper established some new inequalities for the three functions $2\left( \sin x\right) /x+\left( \tan x\right) /x$, $\left( \sin x\right) /x+2\left( \tan (x/2)\right) /\left( x/2\right) $ and $2x/\sin x+x/\tan x$ bounded by the powers of tangent function.

Keywords

circular functions , refinements of the Huygens-type inequalities , even-indexed Bernoulli number , Euler number

Supporting Institution

the National Natural Science Foundation of China (no. 61772025). The second author was supported in part by the Serbian Ministry of Education, Science and Technological Development, under projects ON 174032 and III 44006.

Project Number

the National Natural Science Foundation of China (no. 61772025). The second author was supported in part by the Serbian Ministry of Education, Science and Technological Development, under projects ON 174032 and III 44006.

Thanks

The authors are grateful to anonymous referees for their careful corrections to and valuable comments on the original version of this paper.

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