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On New Generalized Mitrinović-Adamović-Type Inequalities

Author

Listed:
  • Yogesh J. Bagul

    (Department of Mathematics, K. K. M. College, Manwath 431505, India)

  • Wei-Shih Du

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824004, Taiwan)

Abstract

In this paper, we establish new generalized Mitrinović-Adamović-type inequalities in a wider range ( 0 , π ) by using the monotonicity of certain functions. These inequalities contain sharp and tractable bounds for the function sin x x 3 . All the main results are also true in ( − π , 0 ) due to the symmetry of the curves involved.

Suggested Citation

  • Yogesh J. Bagul & Wei-Shih Du, 2025. "On New Generalized Mitrinović-Adamović-Type Inequalities," Mathematics, MDPI, vol. 13(7), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1174-:d:1626796
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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. Nenezić, Marija & Malešević, Branko & Mortici, Cristinel, 2016. "New approximations of some expressions involving trigonometric functions," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 299-315.
    3. Lina Zhang & Xuesi Ma & Dimitri Mugnai, 2021. "Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, April.
    4. Zhen-Hang Yang & Yu-Ming Chu, 2014. "A Note on Jordan, Adamović‐Mitrinović, and Cusa Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. 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, John Wiley & Sons, vol. 2014(1).
    6. Zhen-Hang Yang & Yun-Liang Jiang & Ying-Qing Song & Yu-Ming Chu, 2014. "Sharp Inequalities for Trigonometric Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-18, July.
    7. Zhen-Hang Yang & Yu-Ming Chu, 2014. "A Note on Jordan, Adamović-Mitrinović, and Cusa Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, March.
    8. Zhen-Hang Yang & Yun-Liang Jiang & Ying-Qing Song & Yu-Ming Chu, 2014. "Sharp Inequalities for Trigonometric Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    Full references (including those not matched with items on IDEAS)

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