IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v298y2025i3p871-885.html
   My bibliography  Save this article

Simultaneous approximation by neural network operators with applications to Voronovskaja formulas

Author

Listed:
  • Marco Cantarini
  • Danilo Costarelli

Abstract

In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well‐known neural network (NN) operators activated by the sigmoidal function. Other than a uniform convergence theorem for the derivatives of NN operators, we also provide a quantitative estimate for the order of approximation based on the modulus of continuity of the approximated derivative. Furthermore, a qualitative and quantitative Voronovskaja‐type formula is established, which provides information about the high order of approximation that can be achieved by NN operators. To prove the above theorems, several auxiliary results involving sigmoidal functions have been established. At the end of the paper, noteworthy examples have been discussed in detail.

Suggested Citation

  • Marco Cantarini & Danilo Costarelli, 2025. "Simultaneous approximation by neural network operators with applications to Voronovskaja formulas," Mathematische Nachrichten, Wiley Blackwell, vol. 298(3), pages 871-885, March.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:3:p:871-885
    DOI: 10.1002/mana.202400281
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202400281
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202400281?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
    ---><---

    More about this item

    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:bla:mathna:v:298:y:2025:i:3:p:871-885. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.