On generalization of D’Aurizio-Sándor inequalities involving a parameter. (English) Zbl 1403.26021
Summary: In this work, we generalize the D’Aurizio-Sándor inequalities [J. D’Aurizio, Math. Inequal. Appl. 17, No. 4, 1487–1498 (2014; Zbl 1304.26014); J. Sándor, J. Math. Inequal. 10, No. 3, 885–888 (2016; Zbl 1349.26035)] using an elementary approach. In particular, our approach provides an alternative proof of the D’Aurizio-Sándor inequalities. Moreover, as an immediate consequence of the generalized D’Aurizio-Sándor inequalities, we establish the D’Aurizio-Sándor-type inequalities for hyperbolic functions.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26D05 | Inequalities for trigonometric functions and polynomials |
References:
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| [2] | J. D’AURIZIO, Refinements of the Shafer-Fink inequality of arbitrary uniform precision, Math. Inequal. Appl. 17, 4 (2014), 1487–1498. · Zbl 1304.26014 |
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| [4] | J. S ´ANDOR, On D’Aurizio’s trigonometric inequality, J. Math. Inequal. 10, 3 (2016), 885–888. · Zbl 1349.26035 |
| [5] | J. S ´ANDOR, Extensions of D’Aurizio’s trigonometric inequality, Notes on Number Theory and Discrete Mathematics 23, 2 (2017), 81–83. · Zbl 1387.26046 |
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