IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3104-d693050.html
   My bibliography  Save this article

Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

Author

Listed:
  • Slavko Simić

    (Mathematical Institute SANU, 11000 Belgrade, Serbia)

  • Vesna Todorčević

    (Mathematical Institute SANU, 11000 Belgrade, Serbia
    Department of Mathematics, Faculty of Organizational Sciences, University of Belgrade, 11000 Belgrade, Serbia)

Abstract

In this article, we give sharp two-sided bounds for the generalized Jensen functional J n ( f , g , h ; p , x ). Assuming convexity/concavity of the generating function h , we give exact bounds for the generalized quasi-arithmetic mean A n ( h ; p , x ). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained.

Suggested Citation

  • Slavko Simić & Vesna Todorčević, 2021. "Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities," Mathematics, MDPI, vol. 9(23), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3104-:d:693050
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3104/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3104/
    Download Restriction: no
    ---><---

    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:23:p:3104-:d:693050. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.