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On Jordan’s inequality

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Abstract

We present sharp upper and lower bounds for the function \(\sin (x)/x\). Our bounds are polynomials of degree 2n, where n is any nonnegative integer.

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References

  1. G.D. Anderson, M.K. Vamanamurthy, M.K. Vuorinen, Conformal Invariants, Inequalities, and Quasiconformal Maps (Wiley, New York, 1997)

    MATH  Google Scholar 

  2. G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities (Cambridge University Press, Cambridge, 1952)

    MATH  Google Scholar 

  3. R. Klén, M. Visuri, M. Vuorinen, On Jordan type inequalities for hyperbolic functions. J. Inequal. Appl. 362548, 14 (2010)

    MathSciNet  MATH  Google Scholar 

  4. M.K. Kwong, On Hopital-style rules for monotonicity and oscillation, arXiv:1502.07805 [math.CA] (2015)

  5. J.-L. Li, Y.-L. Li, On the strengthened Jordan’s inequality. J. Inequal. Appl. 74328, 8 (2007)

    MathSciNet  MATH  Google Scholar 

  6. Y. Lv, G. Wang, Y. Chu, A note on Jordan type inequalities for hyperbolic functions. Appl. Math. Lett. 25, 505–508 (2012)

    Article  MathSciNet  Google Scholar 

  7. D.S. Mitrinović, Analytic Inequalities (Springer, New York, 1970)

    Book  Google Scholar 

  8. A.Y. Özban, A new refined form of Jordan’s inequality and its applications. Appl. Math. Lett. 19, 155–160 (2006)

    Article  MathSciNet  Google Scholar 

  9. S. Wu, L. Debnath, Jordan-type inequalities for differentiable functions and their applications. Appl. Math. Lett. 21, 803–809 (2008)

    Article  MathSciNet  Google Scholar 

  10. L. Zhu, A general refinement of Jordan-type inequality. Comp. Math. Appl. 55, 2498–2505 (2008)

    Article  MathSciNet  Google Scholar 

  11. L. Zhu, A source of inequalities for circular functions. Comp. Math. Appl. 58, 1998–2004 (2009)

    Article  MathSciNet  Google Scholar 

  12. L. Zhu, Sharpening Redheffer-type inequalities for circular functions. Appl. Math. Lett. 22, 743–748 (2009)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We thank the referee for helpful comments.

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Correspondence to Horst Alzer.

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Man Kam Kwong: The research of this author is supported by the Hong Kong Government GRF Grant PolyU 5003/12P and the Hong Kong Polytechnic University Grants G-UC22 and G-UA10.

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Alzer, H., Kwong, M.K. On Jordan���s inequality. Period Math Hung 77, 191–200 (2018). https://doi.org/10.1007/s10998-017-0230-z

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  • DOI: https://doi.org/10.1007/s10998-017-0230-z

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