This paper established two new Wilker’s inequalities of exponential type for the functions $$\left( \left( \sin x\right) /x\right) ^{2}+\left( \tan x\right) /x-2$$ sin x / x 2 + tan x / x - 2 and $$\left( x/\left( \sin x\right) \right) ^{2}+x/\left( \tan x\right) -2$$ x / sin x 2 + x / tan x - 2 bounded by the functions $$\begin{aligned} \frac{8}{45}x^{4}\left( \frac{\tan (\sqrt{61}x/7)}{\sqrt{61}x/7}\right) ^{42/61} \end{aligned}$$ 8 45 x 4 tan ( 61 x / 7 ) 61 x / 7 42 / 61 and $$\begin{aligned} \frac{2}{45}x^{4}\left( \frac{\tan \left( \sqrt{46}x/14\right) }{\sqrt{46}x/14}\right) ^{56/23}, \end{aligned}$$ 2 45 x 4 tan 46 x / 14 46 x / 14 56 / 23 , respectively.

中文翻译：

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循环函数的指数型 Wilker 不等式

本文为函数$$\left( \left( \sin x\right) /x\right) ^{2}+\left( \tan x\right) /x-2 建立了两个新的指数型威尔克不等式$$ sin x / x 2 + tan x / x - 2 和 $$\left( x/\left( \sin x\right) \right) ^{2}+x/\left( \tan x\right) -2$$ x / sin x 2 + x / tan x - 2 由函数 $$\begin{aligned} \frac{8}{45}x^{4}\left( \frac{\tan (\ sqrt{61}x/7)}{\sqrt{61}x/7}\right) ^{42/61} \end{aligned}$$ 8 45 x 4 tan ( 61 x / 7 ) 61 x / 7 42 / 61 和 $$\begin{aligned} \frac{2}{45}x^{4}\left( \frac{\tan \left( \sqrt{46}x/14\right) }{\sqrt {46}x/14}\right) ^{56/23}, \end{aligned}$$ 2 45 x 4 tan 46 x / 14 46 x / 14 56 / 23 分别。