IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v200y2025ip1s096007792500949x.html

Fractional integral approaches to weighted corrected Euler–Maclaurin-type inequalities for different classes of functions

Author

Listed:
  • Demir, İzzettin
  • Üneş, Esra

Abstract

In recent years, a wide variety of integral inequalities, including Newton-type, Simpson-type, and corrected Euler–Maclaurin-type inequalities, have been extensively studied, particularly in the framework of fractional calculus using Riemann–Liouville or conformable fractional integrals. Among these, fractional corrected Euler–Maclaurin-type inequalities have emerged as a valuable tool due to their improved approximation capabilities. In this study, we focus on developing weighted corrected Euler–Maclaurin-type inequalities for different classes of functions using Riemann–Liouville fractional integrals. To achieve this, we first derive a key integral equality with the aid of a positive weighted function, providing the foundation for the primary outcomes. Through the use of this integral equality, we prove new inequalities for differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. Also, for better explanation, we offer some examples together with their matching graphs. Moreover, these findings extend previous results. Consequently, the study clarifies the significance of corrected Euler–Maclaurin-type inequalities and suggests opportunities for further exploration.

Suggested Citation

  • Demir, İzzettin & Üneş, Esra, 2025. "Fractional integral approaches to weighted corrected Euler–Maclaurin-type inequalities for different classes of functions," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p1:s096007792500949x
    DOI: 10.1016/j.chaos.2025.116936
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792500949X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116936?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    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. Yun Long & Tingsong Du, 2025. "ANALYSIS ON MULTIPLICATIVE k-ATANGANA–BALEANU FRACTIONAL INTEGRALS WITH APPLICATION TO VARIOUS MERCER-TYPE INEQUALITIES," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-37.
    3. Saad Ihsan Butt & Dawood Khan & Shilpi Jain & Georgia Irina Oros & Praveen Agarwal & Shaher Momani, 2025. "Fractional Integral Inequalities For Superquadratic Functions Via Atangana–Baleanu’S Operator With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(08), pages 1-24.
    4. Badreddine Meftah & Hamid Boulares & Ramsha Shafqat & A. Ben Makhlouf & Ramzi Benaicha & Thanin Sitthiwirattham, 2023. "Some New Fractional Weighted Simpson Type Inequalities for Functions Whose First Derivatives Are Convex," Mathematical Problems in Engineering, Hindawi, vol. 2023, pages 1-19, September.
    5. Almoneef, Areej A. & Hyder, Abd-Allah & Budak, Hüseyin, 2024. "Deriving weighted Newton-type inequalities for diverse function classes through Riemann–Liouville fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    6. Arslan Munir & Miguel Vivas-Cortez & Ather Qayyum & Hüseyin Budak & Irza Faiz & Siti Suzlin Supadi, 2024. "Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 30(1), pages 543-566, December.
    7. Shilpi Jain & Rahul Goyal & Praveen Agarwal & Juan L. G. Guirao, 2021. "Some Inequalities of Extended Hypergeometric Functions," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
    8. Dingyi Ai & Tingsong Du, 2025. "A Study On Newton-Type Inequalities Bounds For Twice ˆ—Differentiable Functions Under Multiplicative Katugampola Fractional Integrals," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-36.
    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. Du, Tingsong & Zhou, Ziyi & Tan, Zongrui, 2025. "Hadamard functional integral operators within fractional multiplicative calculus," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    2. Zhang, Xiaohua & Peng, Yu & Du, Tingsong, 2025. "(k,s)-fractional integral operators in multiplicative calculus," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    3. 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.
    4. Wedad Saleh & Badreddine Meftah & Muhammad Uzair Awan & Abdelghani Lakhdari, 2025. "On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities," Mathematics, MDPI, vol. 13(10), pages 1-34, May.
    5. Almoneef, Areej A. & Hyder, Abd-Allah & Budak, Hüseyin, 2024. "Deriving weighted Newton-type inequalities for diverse function classes through Riemann–Liouville fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    6. Bas, Umut & Akkurt, Abdullah & Has, Aykut & Yildirim, Huseyin, 2025. "Multiplicative Riemann–Liouville fractional integrals and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:chsofr:v:200:y:2025:i:p1:s096007792500949x. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.