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New Polynomial Bounds for Jordan’s and Kober’s Inequalities Based on the Interpolation and Approximation Method

Author

Listed:
  • Lina Zhang

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

  • Xuesi Ma

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

Abstract

In this paper, new refinements and improvements of Jordan’s and Kober’s inequalities are presented. We give new polynomial bounds for the s i n c ( x ) and cos ( x ) functions based on the interpolation and approximation method. The results show that our bounds are tighter than the previous methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:746-:d:257939
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    References listed on IDEAS

    as
    1. Lina Zhang & Xuesi Ma, 2018. "New Refinements and Improvements of Jordan’s Inequality," Mathematics, MDPI, vol. 6(12), pages 1-8, November.
    2. 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.
    3. 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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