Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 134—139
Download full paper: PDF, 155 Kb
Download corrigendum: PDF, 275 Kb
Authors and affiliations
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.
- Trigonometric functions
- Hyperbolic functions
- Iyengar–Madhava Rao–Nanjundiah inequality
- Adamović–Mitrinović inequality
- Lazarović inequality
- l’Hospital rule of monotonicity
2010 Mathematics Subject Classification
- 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- Sándor, J. (2010) Unpublished manuscripts.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 Mitrinović–Adamović 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.
- Sándor, J. (2020). Corrigendum to “On the Iyengar–Madhava Rao–Nanjundiah inequality and its hyperbolic version” [Notes on Number Theory and Discrete Mathematics, Vol. 24, 2018, No. 2, 134–139]. Notes on Number Theory and Discrete Mathematics, 26(1), 230, doi: 10.7546/nntdm.2020.26.1.230.
Cite this paper
Sándor, 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.