IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v33y2025i05ns0218348x2550032x.html
   My bibliography  Save this article

A Study On Newton-Type Inequalities Bounds For Twice ˆ—Differentiable Functions Under Multiplicative Katugampola Fractional Integrals

Author

Listed:
  • DINGYI AI

    (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

In this study, we are particularly drawn to investigating Newton-type inequalities for twice ∗differentiable functions, which are based on multiplicative Katugampola fractional integrals. Toward this goal, we introduce a multiplicative Katugampola fractional identity, forming the basis upon which we establish a sequence of Newton-type inequalities. The derivation of these inequalities is conditioned on Υ∗∗ being multiplicatively convex or (lnΥ∗∗)v being convex for v > 1, with a specific concentration on the case where 0 < v ≤ 1. To help readers fully comprehend the results, we provide illustrative examples and corresponding graphs that validate the derived inequalities. Finally, we showcase the applications of the obtained inequalities in quadrature formulas and special means.

Suggested Citation

  • Dingyi Ai & Tingsong Du, 2025. "A Study On Newton-Type Inequalities Bounds For Twice ˆ—Differentiable Functions Under Multiplicative Katugampola Fractional Integrals," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-36.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:05:n:s0218348x2550032x
    DOI: 10.1142/S0218348X2550032X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X2550032X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X2550032X?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:33:y:2025:i:05:n:s0218348x2550032x. 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.