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
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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.

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Cite this paper

APA

Sándor, J. (2017). Two Applications of the Hadamard Integral Inequality. Notes on Number Theory and Discrete Mathematics, 23(4), 52-55.

Chicago

Sándor, József. “Two Applications of the Hadamard Integral Inequality.” Notes on Number Theory and Discrete Mathematics 23, no. 4 (2017): 52-55.

MLA

Sándor, József. “Two applications of the Hadamard integral inequality.” Notes on Number Theory and Discrete Mathematics 23.4 (2017): 52-55. Print.

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