IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i1p73-d304706.html
   My bibliography  Save this article

On a New Extended Hardy–Hilbert’s Inequality with Parameters

Author

Listed:
  • Bicheng Yang

    (Institute of Applied Mathematics, Longyan University, Longyan 364012, China)

  • Shanhe Wu

    (Department of Mathematics, Longyan University, Longyan 364012, China)

  • Jianquan Liao

    (Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China)

Abstract

In this paper, by introducing parameters and weight functions, with the help of the Euler–Maclaurin summation formula, we establish the extension of Hardy–Hilbert’s inequality and its equivalent forms. The equivalent statements of the best possible constant factor related to several parameters are provided. The operator expressions and some particular cases are also discussed.

Suggested Citation

  • Bicheng Yang & Shanhe Wu & Jianquan Liao, 2020. "On a New Extended Hardy–Hilbert’s Inequality with Parameters," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:73-:d:304706
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/1/73/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/1/73/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael Th. Rassias & Bicheng Yang, 2018. "On a Hilbert-Type Integral Inequality in the Whole Plane," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Applications of Nonlinear Analysis, pages 665-679, Springer.
    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. Bicheng Yang & Shanhe Wu & Aizhen Wang, 2019. "On a Reverse Half-Discrete Hardy-Hilbert’s Inequality with Parameters," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    2. Jianquan Liao & Shanhe Wu & Bicheng Yang, 2020. "On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums," Mathematics, MDPI, vol. 8(2), pages 1-12, February.

    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:8:y:2020:i:1:p:73-:d:304706. 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.