A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $
In this note, we derive an equation which describes the closure of a particular set comprising $n-$valued functions. This result provides an answer to a long standing question for which the particular case $n=2$ had been known and used frequently in the optimal control problems.
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.520/ |
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| author | Zivari-Rezapour, Mohsen Liu, Yichen Emamizadeh, Behrouz |
| author_facet | Zivari-Rezapour, Mohsen Liu, Yichen Emamizadeh, Behrouz |
| author_sort | Zivari-Rezapour, Mohsen |
| collection | DOAJ |
| description | In this note, we derive an equation which describes the closure of a particular set comprising $n-$valued functions. This result provides an answer to a long standing question for which the particular case $n=2$ had been known and used frequently in the optimal control problems. |
| format | Article |
| id | doaj-art-dc9bad77527a4cd582a015faf4300dd9 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-dc9bad77527a4cd582a015faf4300dd92025-02-07T11:11:47ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G101635163910.5802/crmath.52010.5802/crmath.520A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $Zivari-Rezapour, Mohsen0Liu, Yichen1Emamizadeh, Behrouz2Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranDepartment of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, ChinaDepartment of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, China; Institute for Research in Fundamental Sciences (IPM), Tehran, IranIn this note, we derive an equation which describes the closure of a particular set comprising $n-$valued functions. This result provides an answer to a long standing question for which the particular case $n=2$ had been known and used frequently in the optimal control problems.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.520/$n-$valued functionsformulationweak$^\star $ closurerearrangementseigenvalues |
| spellingShingle | Zivari-Rezapour, Mohsen Liu, Yichen Emamizadeh, Behrouz A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $ Comptes Rendus. Mathématique $n-$valued functions formulation weak$^\star $ closure rearrangements eigenvalues |
| title | A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $ |
| title_full | A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $ |
| title_fullStr | A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $ |
| title_full_unstemmed | A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $ |
| title_short | A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $ |
| title_sort | formula for the sum of n weak star closed sets in l infty |
| topic | $n-$valued functions formulation weak$^\star $ closure rearrangements eigenvalues |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.520/ |
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