Two applications of the Hadamard integral inequality

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 4, Pages 52–55
Full paper (PDF, 133 Kb)

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Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University
Cluj-Napoca, Romania

Abstract

As applications of the Hadamard integral inequality, we offer two inequalities for trigonometric, resp. hyperbolic functions. One of results gives a new proof of the Iyengar–Madhava Rao–Nanjundiah inequality for (sin x / x).

Keywords

• BInequalities
• Trigonometric functions
• Hyperbolic functions
• Hadamard’s integral inequality
• Iyengar–Madhava Rao–Nanjundiah inequality
• Adamovic–Mitrinovic inequality

AMS Classification

• 26D05
• 26D07
• 26D15
• 26D99

References

1. Iyengar, K. S. K., Madhava Rao, B. S., & Nanjundiah, T. S. (1945) Some trigonometrical inequalities, Half-Yearly J. Mysore Univ. Sect. B., NS, 6, 1–12.
2. Mitrinovic, D. S. (1970) Analytic inequalities, Springer–Verlag, Berlin.
3. Sándor, J. (2005) On the concavity of (sin x / x) ; Octogon Math. Mag., 13(1), 406–407.