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New Refinements and Improvements of Jordan’s Inequality

Author

Listed:
  • Lina Zhang

    (School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China)

  • Xuesi Ma

    (School of Mathematic and Information Science, Henan Polytechnic University, Jiaozuo 454000, China)

Abstract

The polynomial bounds of Jordan’s inequality, especially the cubic and quartic polynomial bounds, have been studied and improved in a lot of the literature; however, the linear and quadratic polynomial bounds can not be improved very much. In this paper, new refinements and improvements of Jordan’s inequality are given. We present new lower bounds and upper bounds for strengthened Jordan’s inequality using polynomials of degrees 1 and 2. Our bounds are tighter than the previous results of polynomials of degrees 1 and 2. More importantly, we give new improvements of Jordan’s inequality using polynomials of degree 5, which can achieve much tighter bounds than those previous methods.

Suggested Citation

  • Lina Zhang & Xuesi Ma, 2018. "New Refinements and Improvements of Jordan’s Inequality," Mathematics, MDPI, vol. 6(12), pages 1-8, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:284-:d:185627
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    References listed on IDEAS

    as
    1. Alzer, Horst & Kwong, Man Kam, 2016. "Sharp upper and lower bounds for a sine polynomial," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 81-85.
    2. Nishizawa, Yusuke, 2015. "Sharpening of Jordan’s type and Shafer–Fink’s type inequalities with exponential approximations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 146-154.
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    Cited by:

    1. Lina Zhang & Xuesi Ma, 2019. "New Polynomial Bounds for Jordan’s and Kober’s Inequalities Based on the Interpolation and Approximation Method," Mathematics, MDPI, vol. 7(8), pages 1-9, August.

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