On the Iyengar–Madhava Rao–Nanjundiah inequality and its hyperbolic version

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 134–139
DOI: 10.7546/nntdm.2018.24.2.134-139
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Authors and affiliations

József Sándor
Department of Mathematics, Babes–Bolyai University
Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania

Abstract

We provide a new proof of the trigonometric inequality obtained by K. S. K. Iyengar, B. S. Madhava Rao and T. S. Nanjundiah in 1945, and offer also the hyperbolic version of this result. Certain related results are pointed out, too.

Keywords

• Inequalities
• Trigonometric functions
• Hyperbolic functions
• Iyengar–Madhava Rao–Nanjundiah inequality
• Adamović–Mitrinović inequality
• Lazarović inequality
• l’Hospital rule of monotonicity

2010 Mathematics Subject 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. B(N.S.), 6, 1–12.
2. Mitrinovic, D. S. (1970) Analytic Inequalities, Springer–Verlag, Berlin
3. Pinelis, I. (2002) L’Hospital type rules for monotonicity, with applications, J. Ineq. Pure Appl. Math., 3 (1), article 5 (electronic).
4. Sándor, J. (2011) Trigonometric and hyperbolic inequalities, arXiv: 1105.0859v1, 1–93.
5. Sándor, J. (2010) Unpublished manuscripts.
6. Sándor, J. (2017) Refinements of the Mitrinović–Adamović inequality, and an application. Notes on Number Theory and Discrete Mathematics, 23 (1), 4–6.
7. Sándor, J. (2017). Two Applications of the Hadamard Integral Inequality. Notes on Number Theory and Discrete Mathematics, 23 (4), 52–55.