IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p2066-d447752.html
   My bibliography  Save this article

Primal Lower Nice Functions in Reflexive Smooth Banach Spaces

Author

Listed:
  • Messaoud Bounkhel

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Mostafa Bachar

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

In the present work, we extend, to the setting of reflexive smooth Banach spaces, the class of primal lower nice functions, which was proposed, for the first time, in finite dimensional spaces in [Nonlinear Anal. 1991, 17, 385–398] and enlarged to Hilbert spaces in [Trans. Am. Math. Soc. 1995, 347, 1269–1294]. Our principal target is to extend some existing characterisations of this class to our Banach space setting and to study the relationship between this concept and the generalised V -prox-regularity of the epigraphs in the sense proposed recently by the authors in [J. Math. Anal. Appl. 2019, 475, 699–29].

Suggested Citation

  • Messaoud Bounkhel & Mostafa Bachar, 2020. "Primal Lower Nice Functions in Reflexive Smooth Banach Spaces," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2066-:d:447752
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/2066/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/2066/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Messaoud Bounkhel, 2012. "Regularity Concepts in Nonsmooth Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4614-1019-5, June.
    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.
    1. Florent Nacry & Vo Anh Thuong Nguyen & Juliette Venel, 2024. "Metric Subregularity and $$\omega (\cdot )$$ ω ( · ) -Normal Regularity Properties," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1439-1470, November.
    2. Abderrahim Jourani & Emilio Vilches, 2017. "Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 91-116, April.

    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:8:y:2020:i:11:p:2066-:d:447752. 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.