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Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via ( p , q )-Calculus

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  • Julalak Prabseang

    (Department of Mathematics, Faculty of Science and Technology, Phetchaburi Rajabhat University, Phetchaburi 76000, 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 present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using ( p , q ) -calculus. Moreover, we study some new ( p , q ) -Hermite–Hadamard inequalities for multiple integrals. Many results given in this paper provide extensions of others given in previous research.

Suggested Citation

  • Julalak Prabseang & Kamsing Nonlaopon & Jessada Tariboon & Sotiris K. Ntouyas, 2021. "Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via ( p , q )-Calculus," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:446-:d:504287
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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. Yu-Ming Chu & Muhammad Uzair Awan & Sadia Talib & Sabah Iftikhar & Latifa Riahi & Ghulam Shabbir, 2020. "Some New Postquantum Integral Inequalities," Journal of Mathematics, Hindawi, vol. 2020, pages 1-10, November.
    3. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "On (p, q)-analogue of Bernstein operators," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 874-882.
    4. Humaira Kalsoom & Muhammad Amer & Moin-ud-Din Junjua & Sabir Hussain & Gullnaz Shahzadi, 2019. "Some ( p , q )-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions," Mathematics, MDPI, vol. 7(8), pages 1-22, July.
    5. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "Some approximation results by (p, q)-analogue of Bernstein–Stancu operators," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 392-402.
    6. 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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