IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i3p382-d1325800.html
   My bibliography  Save this article

Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems

Author

Listed:
  • Abdullah Ali H. Ahmadini

    (Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia)

  • Waqar Afzal

    (Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
    Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan)

  • Mujahid Abbas

    (Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
    Department of Medical Research, China Medical University, Taichung 406040, Taiwan
    Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa)

  • Elkhateeb S. Aly

    (Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia)

Abstract

This note introduces a new class of preinvexity called ( h 1 , h 2 ) -Godunova-Levin preinvex functions that generalize earlier findings. Based on these notions, we developed Hermite-Hadamard, weighted Fejér, and trapezium type inequalities. Furthermore, we constructed some non-trivial examples in order to verify all the developed results. In addition, we discussed some applications related to the trapezoidal formula, probability density functions, special functions and special means. Lastly, we discussed the importance of order relations and left two open problems for future research. As an additional benefit, we believe that the present work can provide a strong catalyst for enhancing similar existing literature.

Suggested Citation

  • Abdullah Ali H. Ahmadini & Waqar Afzal & Mujahid Abbas & Elkhateeb S. Aly, 2024. "Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems," Mathematics, MDPI, vol. 12(3), pages 1-28, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:382-:d:1325800
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/3/382/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/3/382/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shilpi Jain & Khaled Mehrez & Dumitru Baleanu & Praveen Agarwal, 2019. "Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    2. Peide Liu & Muhammad Bilal Khan & Muhammad Aslam Noor & Khalida Inayat Noor & Kaleem R. Kazmi, 2021. "On Strongly Generalized Preinvex Fuzzy Mappings," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, April.
    3. Waqar Afzal & Khurram Shabbir & Mubashar Arshad & Joshua Kiddy K. Asamoah & Ahmed M. Galal & Ching-Feng Wen, 2023. "Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation," Journal of Mathematics, Hindawi, vol. 2023, pages 1-14, June.
    4. Xiaoju Zhang & Khurram Shabbir & Waqar Afzal & He Xiao & Dong Lin & Xiaolong Qin, 2022. "Hermite–Hadamard and Jensen-Type Inequalities via Riemann Integral Operator for a Generalized Class of Godunova–Levin Functions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, August.
    5. Gavrea, Bogdan, 2015. "A Hermite–Hadamard type inequality with applications to the estimation of moments of continuous random variables," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 92-98.
    6. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    7. Yu, Yuping & Liu, Jun & Du, Tingsong, 2022. "Certain error bounds on the parameterized integral inequalities in the sense of fractal sets," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    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. Waqar Afzal & Mujahid Abbas & Omar Mutab Alsalami, 2024. "Bounds of Different Integral Operators in Tensorial Hilbert and Variable Exponent Function Spaces," Mathematics, MDPI, vol. 12(16), pages 1-33, August.
    2. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    3. Waqar Afzal & Daniel Breaz & Mujahid Abbas & Luminiţa-Ioana Cotîrlă & Zareen A. Khan & Eleonora Rapeanu, 2024. "Hyers–Ulam Stability of 2 D -Convex Mappings and Some Related New Hermite–Hadamard, Pachpatte, and Fejér Type Integral Inequalities Using Novel Fractional Integral Operators via Totally Interval-Order," Mathematics, MDPI, vol. 12(8), pages 1-34, April.
    4. Çi̇ri̇ş, Sümeyye Ermeydan & Yildirim, Hüseyin, 2024. "Hermite–Hadamard inequalities for generalized σ−conformable integrals generated by co-ordinated functions," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

    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:12:y:2024:i:3:p:382-:d:1325800. 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.