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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
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    References listed on IDEAS

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    1. Messaoud Bounkhel, 2012. "Regularity Concepts in Nonsmooth Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4614-1019-5, August.
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