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Simpson- and Newton-Type Inequalities for Convex Functions via ( p , q )-Calculus

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)

Abstract

In this paper, we establish several new ( p , q ) -integral identities involving ( p , q ) -integrals by using the definition of a ( p , q ) -derivative. These results are then used to derive ( p , q ) -integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results.

Suggested Citation

  • Waewta Luangboon & Kamsing Nonlaopon & Jessada Tariboon & Sotiris K. Ntouyas, 2021. "Simpson- and Newton-Type Inequalities for Convex Functions via ( p , q )-Calculus," Mathematics, MDPI, vol. 9(12), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1338-:d:572056
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    References listed on IDEAS

    as
    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. Yongping Deng & Muhammad Uzair Awan & Shanhe Wu, 2019. "Quantum Integral Inequalities of Simpson-Type for Strongly Preinvex Functions," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    3. 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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