IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i04ns0218348x22500840.html
   My bibliography  Save this article

PROPERTIES AND INTEGRAL INEQUALITIES ARISING FROM THE GENERALIZED n-POLYNOMIAL CONVEXITY IN THE FRAME OF FRACTAL SPACE

Author

Listed:
  • LEI XU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China)

  • SHUHONG YU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China)

  • TINGSONG DU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China)

Abstract

First, we define what we named the generalized n-polynomial convex mappings as a generalization of convex mappings, investigate their meaningful properties, and establish two Hermite–Hadamard’s-type integral inequalities via the newly proposed mappings in the frame of fractal space as well. Second, in accordance with the discovered identity with a parameter, we present certain improved integral inequalities with regard to the mappings whose first-order derivatives in absolute value belong to the generalized n-polynomial convexity. As applications, on the basis of local fractional calculus, we acquire three inequalities in view of special means, numerical integrations, as well as probability density mappings, respectively.

Suggested Citation

  • Lei Xu & Shuhong Yu & Tingsong Du, 2022. "PROPERTIES AND INTEGRAL INEQUALITIES ARISING FROM THE GENERALIZED n-POLYNOMIAL CONVEXITY IN THE FRAME OF FRACTAL SPACE," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-27, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500840
    DOI: 10.1142/S0218348X22500840
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22500840
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X22500840?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.

    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:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500840. 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/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.