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Some quantum estimates for Hermite–Hadamard inequalities

Author

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  • Noor, Muhammad Aslam
  • Noor, Khalida Inayat
  • Awan, Muhammad Uzair

Abstract

In this paper, we establish quantum analogue of classical integral identity. Using this identity, we derive some quantum estimates for Hermite–Hadamard inequalities for q-differentiable convex functions and q-differentiable quasi convex functions. Results obtained present refinement and improvement of the known results. The ideas and techniques of this paper may stimulate further research.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:675-679
    DOI: 10.1016/j.amc.2014.11.090
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    Cited by:

    1. Miguel J. Vivas-Cortez & Rozana Liko & Artion Kashuri & Jorge E. Hernández Hernández, 2019. "New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ -Convex Functions," Mathematics, MDPI, vol. 7(11), pages 1-19, November.
    2. 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.
    3. Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some quantum integral inequalities via preinvex functions," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 242-251.
    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. Muhammad Aamir Ali & Sotiris K. Ntouyas & Jessada Tariboon, 2021. "Generalization of Quantum Ostrowski-Type Integral Inequalities," Mathematics, MDPI, vol. 9(10), pages 1-8, May.
    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.
    7. 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.
    8. Hefeng Zhuang & Wenjun Liu & Jaekeun Park, 2019. "Some Quantum Estimates of Hermite-Hadamard Inequalities for Quasi-Convex Functions," Mathematics, MDPI, vol. 7(2), pages 1-18, February.
    9. 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.
    10. 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.
    11. 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.
    12. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram, 2020. "On q -Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    13. 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.

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