IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v51y2020i4d10.1007_s13226-020-0495-4.html
   My bibliography  Save this article

The Best Possible Constants of the Inequalities with Power Exponential Functions

Author

Listed:
  • Yusuke Nishizawa

    (Saitama University)

Abstract

The author in [7] conjectured the following inequality; If a and b are nonnegative real numbers with a + b = 1/2, then the inequality 1/2 ≤ a(2b)k+ b(2a)k ≤ 1 holds for 0 ≤ k ≤ 1. In this paper, we shall prove the conjecture affirmatively and give the upper and lower estimation of the power exponential functions ab + ba for the nonnegative real numbers a and b with a + b = 2. Moreover, we pose some inequalities with power exponential functions.

Suggested Citation

  • Yusuke Nishizawa, 2020. "The Best Possible Constants of the Inequalities with Power Exponential Functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1761-1768, December.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0495-4
    DOI: 10.1007/s13226-020-0495-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-020-0495-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-020-0495-4?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Yusuke Nishizawa, 2017. "Symmetric inequalities with power-exponential functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(3), pages 335-344, September.
    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:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0495-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.