IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2023i1p49-d1306036.html
   My bibliography  Save this article

Inequalities in Riemann–Lebesgue Integrability

Author

Listed:
  • Anca Croitoru

    (Faculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, Romania)

  • Alina Gavriluţ

    (Faculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, Romania)

  • Alina Iosif

    (Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploieşti, Bd. Bucureşti, No. 39, 100680 Ploieşti, Romania)

  • Anna Rita Sambucini

    (Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy)

Abstract

In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, in particular for Riemann–Lebesgue integrable interval-valued multifunctions, and obtain some inequalities, such as a Minkowski-type inequality, a Beckenbach-type inequality and some generalizations of Hölder inequalities.

Suggested Citation

  • Anca Croitoru & Alina Gavriluţ & Alina Iosif & Anna Rita Sambucini, 2023. "Inequalities in Riemann–Lebesgue Integrability," Mathematics, MDPI, vol. 12(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:49-:d:1306036
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/49/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/1/49/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Danilo Costarelli & Anca Croitoru & Alina Gavriluţ & Alina Iosif & Anna Rita Sambucini, 2020. "The Riemann-Lebesgue Integral of Interval-Valued Multifunctions," Mathematics, MDPI, vol. 8(12), pages 1-17, December.
    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.

      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:2023:i:1:p:49-:d:1306036. 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.