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On q -Hermite-Hadamard Inequalities for Differentiable Convex Functions

Author

Listed:
  • Seksan Jhanthanam

    (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, 45110 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)

  • Kamsing Nonlaopon

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

Abstract

In this paper, we establish some new results on the left-hand side of the q -Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al ( q -Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:632-:d:249052
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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.
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    Cited by:

    1. Fongchan Wannalookkhee & Kamsing Nonlaopon & Jessada Tariboon & Sotiris K. Ntouyas, 2021. "On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via ( p , q )-Calculus," Mathematics, MDPI, vol. 9(7), pages 1-19, March.
    2. 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.
    3. 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.
    4. 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.
    5. Surang Sitho & Muhammad Aamir Ali & Hüseyin Budak & Sotiris K. Ntouyas & Jessada Tariboon, 2021. "Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus," Mathematics, MDPI, vol. 9(14), pages 1-21, July.
    6. Pimchana Siricharuanun & Samet Erden & Muhammad Aamir Ali & Hüseyin Budak & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2021. "Some New Simpson’s and Newton’s Formulas Type Inequalities for Convex Functions in Quantum Calculus," Mathematics, MDPI, vol. 9(16), pages 1-18, August.

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