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Some ( p , q )-Integral Inequalities of Hermite–Hadamard Inequalities for ( p , q )-Differentiable Convex Functions

Author

Listed:
  • Waewta Luangboon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Jessada Tariboon

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
    Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey)

Abstract

In this paper, we establish a new ( p , q ) b -integral identity involving the first-order ( p , q ) b -derivative. Then, we use this result to prove some new ( p , q ) b -integral inequalities related to Hermite–Hadamard inequalities for ( p , q ) b -differentiable convex functions. Furthermore, our main results are used to study some special cases of various integral inequalities. The newly presented results are proven to be generalizations of some integral inequalities of already published results. Finally, some examples are given to illustrate the investigated results.

Suggested Citation

  • Waewta Luangboon & Kamsing Nonlaopon & Jessada Tariboon & Sotiris K. Ntouyas & Hüseyin Budak, 2022. "Some ( p , q )-Integral Inequalities of Hermite–Hadamard Inequalities for ( p , q )-Differentiable Convex Functions," Mathematics, MDPI, vol. 10(5), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:826-:d:764437
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    References listed on IDEAS

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    1. Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some quantum estimates for Hermite–Hadamard inequalities," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 675-679.
    2. Seksan Jhanthanam & Jessada Tariboon & Sotiris K. Ntouyas & Kamsing Nonlaopon, 2019. "On q -Hermite-Hadamard Inequalities for Differentiable Convex Functions," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
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    Cited by:

    1. Wei Liu & Fangfang Shi & Guoju Ye & Dafang Zhao, 2022. "The Properties of Harmonically cr - h -Convex Function and Its Applications," Mathematics, MDPI, vol. 10(12), pages 1-15, June.

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