V-Proximal Trustworthy Banach Spaces

V-Proximal Trustworthy Banach Spaces

In a recent work (2016), the first author proved the fuzzy sum rule for the V-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large an...

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Main Authors: Messaoud Bounkhel, Mostafa Bachar
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/4274160
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spelling doaj-bca990a7a744431c9878710daad161462020-11-25T02:24:27ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/42741604274160V-Proximal Trustworthy Banach SpacesMessaoud Bounkhel0Mostafa Bachar1Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaIn a recent work (2016), the first author proved the fuzzy sum rule for the V-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all Lp spaces 1<p<∞ as well as the sequence spaces lp1<p<∞, the Sobolev spaces Wp,n1<p<∞, and the Schatten trace ideals Cp1<p<∞.http://dx.doi.org/10.1155/2020/4274160
collection DOAJ
language English
format Article
sources DOAJ
author Messaoud Bounkhel
Mostafa Bachar
spellingShingle Messaoud Bounkhel
Mostafa Bachar
V-Proximal Trustworthy Banach Spaces
Journal of Function Spaces
author_facet Messaoud Bounkhel
Mostafa Bachar
author_sort Messaoud Bounkhel
title V-Proximal Trustworthy Banach Spaces
title_short V-Proximal Trustworthy Banach Spaces
title_full V-Proximal Trustworthy Banach Spaces
title_fullStr V-Proximal Trustworthy Banach Spaces
title_full_unstemmed V-Proximal Trustworthy Banach Spaces
title_sort v-proximal trustworthy banach spaces
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description In a recent work (2016), the first author proved the fuzzy sum rule for the V-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all Lp spaces 1<p<∞ as well as the sequence spaces lp1<p<∞, the Sobolev spaces Wp,n1<p<∞, and the Schatten trace ideals Cp1<p<∞.
url http://dx.doi.org/10.1155/2020/4274160
work_keys_str_mv AT messaoudbounkhel vproximaltrustworthybanachspaces
AT mostafabachar vproximaltrustworthybanachspaces
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