IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i4p446-d504287.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/4/446/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/4/446/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Liang Zeng & Qing-Bo Cai & Xiao-Wei Xu, 2020. "A -Statistical Convergence Properties of Kantorovich Type λ -Bernstein Operators Via ( p , q )-Calculus," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    3. Kanat, K. & Sofyalıoğlu, M., 2018. "Some approximation results for Stancu type Lupaş–Schurer operators based on (p, q)-integers," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 129-142.
    4. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2016. "Erratum to ``On (p, q)-analogue of Bernstein Operators'' [Appl. Math. Comput. 266 (2015) 874–882]," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 70-71.
    5. 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.
    6. 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.
    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. 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.
    9. Cai, Qing-Bo & Zhou, Guorong, 2016. "On (p, q)-analogue of Kantorovich type Bernstein–Stancu–Schurer operators," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 12-20.
    10. 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.
    11. Hari M. Srivastava & Khursheed J. Ansari & Faruk Özger & Zeynep Ödemiş Özger, 2021. "A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    12. Saima Rashid & Muhammad Aslam Noor & Khalida Inayat Noor & Farhat Safdar & Yu-Ming Chu, 2019. "Hermite-Hadamard Type Inequalities for the Class of Convex Functions on Time Scale," Mathematics, MDPI, vol. 7(10), pages 1-20, October.
    13. Mursaleen, M. & Naaz, Ambreen & Khan, Asif, 2019. "Improved approximation and error estimations by King type (p, q)-Szász-Mirakjan Kantorovich operators," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 175-185.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "Corrigendum to: “Some approximation results by (p, q)-analogue of Bernstein–Stancu operators” [Appl. Math. Comput. 264(2015)392–402]," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 744-746.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:446-:d:504287. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.