On Wilker-type inequalities. (English) Zbl 1144.26020

Zhu, Ling

Math. Inequal. Appl. 10, No. 4, 727-731 (2007).

The paper contains a lucid proof of the inequality \(\left( \frac{\sinh x}{x}\right) ^2 +\frac{\tanh x}{x} >2+\frac{8}{45}\tanh x \) valid for positive \(x\). It is also shown that the constant \(8/45\) is the best possible one. The proof is based on the so-called L’Hopital rule of monotonicity.

Reviewer: Mihai Cipu (Bucureşti)

MSC:

26D05	Inequalities for trigonometric functions and polynomials
26D15	Inequalities for sums, series and integrals

Keywords:

Wilker-type inequalities; hyperbolic functions; L’Hopital rule of monotonicity