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New Inequalities of Cusa–Huygens Type

Author

Listed:
  • Ling Zhu

    (Department of Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China)

Abstract

Using the power series expansions of the functions cot x , 1 / sin x and 1 / sin 2 x , and the estimate of the ratio of two adjacent even-indexed Bernoulli numbers, we improve Cusa–Huygens inequality in two directions on 0 , π / 2 . Our results are much better than those in the existing literature.

Suggested Citation

  • Ling Zhu, 2021. "New Inequalities of Cusa–Huygens Type," Mathematics, MDPI, vol. 9(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2101-:d:625908
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    References listed on IDEAS

    as
    1. Zhen-Hang Yang & Yu-Ming Chu & Ying-Qing Song & Yong-Min Li, 2014. "A Sharp Double Inequality for Trigonometric Functions and Its Applications," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    2. Yu-Ming Chu & Miao-Kun Wang & Zi-Kui Wang, 2011. "A Sharp Double Inequality between Harmonic and Identric Means," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-7, October.
    3. Jian-Lin Li, 2006. "An identity related to Jordan's inequality," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-6, October.
    4. Wei-Ming Gong & Ying-Qing Song & Miao-Kun Wang & Yu-Ming Chu, 2012. "A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, September.
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    Cited by:

    1. Ling Zhu, 2021. "New Bounds for the Sine Function and Tangent Function," Mathematics, MDPI, vol. 9(19), pages 1-12, September.

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