A convex-valued selection theorem with a non-separable Banach space
In the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence φ:X→2Y{\varphi:X\to 2^{Y}}. We prove that if φ has either closed or finite-dimensional images, then there admits a continuous single-valued selection, where X is...
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De Gruyter
2018-05-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2016-0053 |
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doaj-0684de1e23084bc893fab71d745a17e82021-09-06T19:39:54ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2018-05-017219720910.1515/anona-2016-0053A convex-valued selection theorem with a non-separable Banach spaceGourdel Pascal0Mâagli Nadia1Paris School of Economics, Université Paris 1 Panthéon–Sorbonne, Centre d’Economie de la Sorbonne–CNRS, 106-112 Boulevard de l’Hôpital, 75647ParisCedex 13, FranceParis School of Economics, Université Paris 1 Panthéon–Sorbonne, Centre d’Economie de la Sorbonne–CNRS, 106-112 Boulevard de l’Hôpital, 75647ParisCedex 13, FranceIn the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence φ:X→2Y{\varphi:X\to 2^{Y}}. We prove that if φ has either closed or finite-dimensional images, then there admits a continuous single-valued selection, where X is a metric space and Y is a Banach space. We provide a geometric and constructive proof of our main result based on the concept of peeling introduced in this paper.https://doi.org/10.1515/anona-2016-0053barycentric coordinatescontinuous selectionslower semicontinuous correspondenceclosed-valued correspondencefinite-dimensional convex valuesseparable banach spaces54c60 54c65 54d65 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Gourdel Pascal Mâagli Nadia |
| spellingShingle |
Gourdel Pascal Mâagli Nadia A convex-valued selection theorem with a non-separable Banach space Advances in Nonlinear Analysis barycentric coordinates continuous selections lower semicontinuous correspondence closed-valued correspondence finite-dimensional convex values separable banach spaces 54c60 54c65 54d65 |
| author_facet |
Gourdel Pascal Mâagli Nadia |
| author_sort |
Gourdel Pascal |
| title |
A convex-valued selection theorem with a non-separable Banach space |
| title_short |
A convex-valued selection theorem with a non-separable Banach space |
| title_full |
A convex-valued selection theorem with a non-separable Banach space |
| title_fullStr |
A convex-valued selection theorem with a non-separable Banach space |
| title_full_unstemmed |
A convex-valued selection theorem with a non-separable Banach space |
| title_sort |
convex-valued selection theorem with a non-separable banach space |
| publisher |
De Gruyter |
| series |
Advances in Nonlinear Analysis |
| issn |
2191-9496 2191-950X |
| publishDate |
2018-05-01 |
| description |
In the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence
φ:X→2Y{\varphi:X\to 2^{Y}}. We prove that if φ has either closed or finite-dimensional images, then there admits a continuous single-valued selection, where X is a metric space and Y is a Banach space. We provide a geometric and constructive proof of our main result based on the concept of peeling introduced in this paper. |
| topic |
barycentric coordinates continuous selections lower semicontinuous correspondence closed-valued correspondence finite-dimensional convex values separable banach spaces 54c60 54c65 54d65 |
| url |
https://doi.org/10.1515/anona-2016-0053 |
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AT gourdelpascal aconvexvaluedselectiontheoremwithanonseparablebanachspace AT maaglinadia aconvexvaluedselectiontheoremwithanonseparablebanachspace AT gourdelpascal convexvaluedselectiontheoremwithanonseparablebanachspace AT maaglinadia convexvaluedselectiontheoremwithanonseparablebanachspace |
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1717769745973903360 |