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Chu, Hong-Hu; Yang, Zhen-Hang; Chu, Yu-Ming; Zhang, Wen

Generalized Wilker-type inequalities with two parameters. (English) Zbl 1342.26039

J. Inequal. Appl. 2016, Paper No. 187, 13 p. (2016).
Summary: In the article, we present certain \(p, q\in\mathbb{R}\) such that the Wilker-type inequalities \[ \begin{aligned} & \frac{2q}{p+2q} \biggl(\frac{\sin x}{x} \biggr)^{p}+ \frac{p}{p+2q} \biggl(\frac{\tan x}{x} \biggr)^{q}>(< )1 \quad \text{ and }\\ & \biggl(\frac{\pi}{2} \biggr)^{p} \biggl(\frac{\sin x}{x} \biggr)^{p}+ \biggl[1- \biggl(\frac{\pi}{2} \biggr)^{p} \biggr] \biggl(\frac{\tan x}{x} \biggr)^{q}>(<)1 \end{aligned} \] hold for all \(x\in(0, \pi/2)\).

Cited in 10 Documents

MSC:

26D05 Inequalities for trigonometric functions and polynomials
33B10 Exponential and trigonometric functions

Keywords:

Wilker inequality; trigonometric function; Bernoulli number; monotonicity
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References:

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