Primal Lower Nice Functions in Reflexive Smooth Banach Spaces
Open Access
- 19 November 2020
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 8 (11), 2066
- https://doi.org/10.3390/math8112066
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
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