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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/4274160 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567826486919168 |
|---|---|
| author | Messaoud Bounkhel Mostafa Bachar |
| author_facet | Messaoud Bounkhel Mostafa Bachar |
| author_sort | Messaoud Bounkhel |
| collection | DOAJ |
| 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<∞. |
| format | Article |
| id | doaj-art-bca990a7a744431c9878710daad16146 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-bca990a7a744431c9878710daad161462025-02-03T01:00:30ZengWileyJournal 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 |
| spellingShingle | Messaoud Bounkhel Mostafa Bachar V-Proximal Trustworthy Banach Spaces Journal of Function Spaces |
| title | 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_short | V-Proximal Trustworthy Banach Spaces |
| title_sort | v proximal trustworthy banach spaces |
| url | http://dx.doi.org/10.1155/2020/4274160 |
| work_keys_str_mv | AT messaoudbounkhel vproximaltrustworthybanachspaces AT mostafabachar vproximaltrustworthybanachspaces |