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Wilker inequalities of exponential type for circular functions

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This paper established two new Wilker’s inequalities of exponential type for the functions \(\left( \left( \sin x\right) /x\right) ^{2}+\left( \tan x\right) /x-2\) and \(\left( x/\left( \sin x\right) \right) ^{2}+x/\left( \tan x\right) -2\) bounded by the functions

$$\begin{aligned} \frac{8}{45}x^{4}\left( \frac{\tan (\sqrt{61}x/7)}{\sqrt{61}x/7}\right) ^{42/61} \end{aligned}$$

and

$$\begin{aligned} \frac{2}{45}x^{4}\left( \frac{\tan \left( \sqrt{46}x/14\right) }{\sqrt{46}x/14}\right) ^{56/23}, \end{aligned}$$

respectively.

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Acknowledgements

The author is thankful to reviewers for reviewers’ valuable comments on the original version of this paper. This paper is supported by the Natural Science Foundation of China Grants No. 61772025.

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

    Ling Zhu

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Zhu, L. Wilker inequalities of exponential type for circular functions. RACSAM 115, 35 (2021). https://doi.org/10.1007/s13398-020-00973-6

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