IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1445-d1099205.html
   My bibliography  Save this article

Continuous Differentiability in the Context of Generalized Approach to Differentiability

Author

Listed:
  • Nikola Koceić-Bilan

    (Faculty of Science, University of Split, 21000 Split, Croatia)

  • Snježana Braić

    (Faculty of Science, University of Split, 21000 Split, Croatia)

Abstract

Recently, in their paper, the authors generalized the notion of differentiability by defining it for all points of the functional domain (not only interior points) in which the notion of differentiability can be considered meaningful. In this paper, the notion of continuous differentiability is introduced for the differentiable function f : X → R m with a not necessarily open domain X ⊆ R n ; i.e., the continuity of the mapping d f : X → H o m R n , R m is considered. In addition to introducing continuous differentiability in the context of this generalized approach to differentiability, its characterization is also given. It is proved that the continuity of derivatives at some not necessarily interior points of the functional domain in the direction of n linearly independent vectors implies (continuous) differentiability.

Suggested Citation

  • Nikola Koceić-Bilan & Snježana Braić, 2023. "Continuous Differentiability in the Context of Generalized Approach to Differentiability," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1445-:d:1099205
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1445/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1445/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nikola Koceić-Bilan & Snježana Braić, 2022. "Generalized Approach to Differentiability," Mathematics, MDPI, vol. 10(17), pages 1-29, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nikola Koceić-Bilan & Ivančica Mirošević, 2023. "The Mean Value Theorem in the Context of Generalized Approach to Differentiability," Mathematics, MDPI, vol. 11(20), pages 1-8, October.

    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. Nikola Koceić-Bilan & Ivančica Mirošević, 2023. "The Mean Value Theorem in the Context of Generalized Approach to Differentiability," Mathematics, MDPI, vol. 11(20), pages 1-8, October.

    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:11:y:2023:i:6:p:1445-:d:1099205. 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.