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Integral Inequalities Involving Strictly Monotone Functions

Author

Listed:
  • Mohamed Jleli

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
    These authors contributed equally to this work.)

  • Bessem Samet

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

Functional inequalities involving special functions are very useful in mathematical analysis, and several interesting results have been obtained in this topic. Several methods have been used by many authors in order to derive upper or lower bounds of certain special functions. In this paper, we establish some general integral inequalities involving strictly monotone functions. Next, some special cases are discussed. In particular, several estimates of trigonometric and hyperbolic functions are deduced. For instance, we show that Mitrinović-Adamović inequality, Lazarevic inequality, and Cusa-Huygens inequality are special cases of our obtained results. Moreover, an application to integral equations is provided.

Suggested Citation

  • Mohamed Jleli & Bessem Samet, 2023. "Integral Inequalities Involving Strictly Monotone Functions," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1873-:d:1124032
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    References listed on IDEAS

    as
    1. 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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