Sharp refined quadratic estimations of Shafer's inequalities

Ling Zhu; Ling Zhu

doi:10.3934/math.2021296

AIMS Mathematics

2021, Volume 6, Issue 5: 5020-5027. doi: 10.3934/math.2021296

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Research article

Sharp refined quadratic estimations of Shafer's inequalities

Ling Zhu ^,

Department of Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang, China

Received: 31 December 2020 Accepted: 25 February 2021 Published: 04 March 2021
MSC : 26D15, 42A10

In this paper, using the power series expansions of $ (\tan x)^{k}(k = 1, 2, 3) $ and the monotonicity of a function involving the Riemann's zeta function, we sharpen the quadratic estimations of Shafer's inequalities which is refined by Nishizawa ^[5].
- Shafer's inequalities,
- upper bound for arctangent,
- lower bound for arctangent,
- best constants
Citation: Ling Zhu. Sharp refined quadratic estimations of Shafer's inequalities[J]. AIMS Mathematics, 2021, 6(5): 5020-5027. doi: 10.3934/math.2021296

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Abstract

In this paper, using the power series expansions of $ (\tan x)^{k}(k = 1, 2, 3) $ and the monotonicity of a function involving the Riemann's zeta function, we sharpen the quadratic estimations of Shafer's inequalities which is refined by Nishizawa ^[5].

References

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