IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i11p1047-d283193.html
   My bibliography  Save this article

New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ -Convex Functions

Author

Listed:
  • Miguel J. Vivas-Cortez

    (Facultad de Ciencias Exactas y Naturales, Escuela de Matemáticas y Físicas, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076. Apartado: 17-01-2184, Quito 170143, Ecuador
    These authors contributed equally to this work.)

  • Rozana Liko

    (Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 1001 Vlora, Albania
    These authors contributed equally to this work.)

  • Artion Kashuri

    (Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 1001 Vlora, Albania
    These authors contributed equally to this work.)

  • Jorge E. Hernández Hernández

    (Decanato de Ciencias Económicas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Barquisimeto 3001, Venezuela
    These authors contributed equally to this work.)

Abstract

In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is provided. The authors also prove an identity for twice q - differentiable functions using Raina’s function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1047-:d:283193
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/11/1047/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/11/1047/
    Download Restriction: no
    ---><---

    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.
    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. 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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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.

    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:7:y:2019:i:11:p:1047-:d:283193. 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.