V-Prox-Regular Functions in Smooth Banach Spaces

In this paper, we continue the study of the V-prox-regularity that we have started recently for sets. We define an appropriate concept of the V-prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship betw...

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Bibliographic Details
Published in:Journal of function spaces Vol. 2020; no. 2020; pp. 1 - 8
Main Authors: Bounkhel, Messaoud, Bachar, Mostafa
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Wiley
Subjects:
Banach spaces
Hilbert space
Inequality
Regularity
ISSN:2314-8896, 2314-8888
Online Access:Get full text
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Summary:In this paper, we continue the study of the V-prox-regularity that we have started recently for sets. We define an appropriate concept of the V-prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship between the V-prox-regularity of a given l.s.c. f and the V-prox-regularity of its epigraph.
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ISSN:2314-8896
2314-8888
DOI:10.1155/2020/9465492