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Keywords = limiting V-proximal subdifferential

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17 pages, 287 KiB  
Article
Primal Lower Nice Functions in Reflexive Smooth Banach Spaces
by Messaoud Bounkhel and Mostafa Bachar
Mathematics 2020, 8(11), 2066; https://doi.org/10.3390/math8112066 - 19 Nov 2020
Cited by 3 | Viewed by 2027
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 [...] Read more.
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]. Full article
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