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On Wilker-type inequalities. (English) Zbl 1144.26020

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.

MSC:

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