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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## Details

### 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
- Adamovi
*ć*–Mitrinovi*ć*inequality - Lazarovi
*ć*inequality - l’Hospital rule of monotonicity

### 2010 Mathematics Subject Classification

- 26D05
- 26D07
- 26D15
- 26D99

### References

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- Sándor, J. (2010) Unpublished manuscripts.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

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## Cite this paper

APASándor, J. (2018). On the Iyengar–Madhava Rao–Nanjundiah inequality and its hyperbolic version. Notes on Number Theory and Discrete Mathematics, 24(2), 134-139, doi: 10.7546/nntdm.2018.24.2.134-139.

ChicagoSándor, József. “On the Iyengar–Madhava Rao–Nanjundiah Inequality and Its Hyperbolic Version.” Notes on Number Theory and Discrete Mathematics 24, no. 2 (2018): 134-139, doi: 10.7546/nntdm.2018.24.2.134-139.

MLASándor, József. “On the Iyengar–Madhava Rao–Nanjundiah Inequality and Its Hyperbolic Version.” Notes on Number Theory and Discrete Mathematics 24.2 (2018): 134-139. Print, doi: 10.7546/nntdm.2018.24.2.134-139.