Primal Lower Nice Functions in Reflexive Smooth Banach Spaces

Messaoud Bounkhel and Mostafa Bachar
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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

Mathematics, 2020, vol. 8, issue 11, 1-17

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].

Keywords: generalised projection; V -proximal subdifferential; V -proximal normal cone; limiting V -proximal subdifferential; generalised prox-regularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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