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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Vydáno v:Journal of function spaces Ročník 2020; číslo 2020; s. 1 - 8
Hlavní autoři: Bounkhel, Messaoud, Bachar, Mostafa
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Wiley
Témata:
Banach spaces
Hilbert space
Inequality
Regularity
ISSN:2314-8896, 2314-8888
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:2314-8896
2314-8888
DOI:10.1155/2020/9465492