IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i14p1666-d594910.html
   My bibliography  Save this article

Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus

Author

Listed:
  • Surang Sitho

    (Department of Social and Applied Science, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Muhammad Aamir Ali

    (Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
    These authors contributed equally to this work.)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

Abstract

In this article, we use quantum integrals to derive Hermite–Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the q ϰ 2 -quantum integral to show midpoint and trapezoidal inequalities for q ϰ 2 -differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite–Hadamard-type inequality for preinvex functions via q ϰ 1 -quantum integral is not valid for preinvex functions, and we present its proper form. We use q ϰ 1 -quantum integrals to show midpoint inequalities for q ϰ 1 -differentiable preinvex functions. It is also demonstrated that by considering the limit q → 1 − and η ϰ 2 , ϰ 1 = − η ϰ 1 , ϰ 2 = ϰ 2 − ϰ 1 in the newly derived results, the newly proved findings can be turned into certain known results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1666-:d:594910
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/14/1666/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/14/1666/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sikander Mehmood & Fiza Zafar & Nusrat Yasmin, 2019. "Hermite-Hadamard-Fejér Type Inequalities for Preinvex Functions Using Fractional Integrals," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
    2. 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.
    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. 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. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    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. Humaira Kalsoom & Zareen A. Khan, 2022. "Hermite-Hadamard-Fejér Type Inequalities with Generalized K -Fractional Conformable Integrals and Their Applications," Mathematics, MDPI, vol. 10(3), pages 1-20, February.
    12. Aglić Aljinović, Andrea & Kovačević, Domagoj & Puljiz, Mate & Žgaljić Keko, Ana, 2021. "On Ostrowski inequality for quantum calculus," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Cristescu, Gabriela & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2016. "Some inequalities for functions having Orlicz-convexity," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 226-236.

    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:14:p:1666-:d:594910. 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.