A viability approach to the inverse set-valued map theorem
Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the tran...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Aubin, Jean-Pierre [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Schlagwörter: |
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| Anmerkung: |
© Birkhäuser Verlag, Basel 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of evolution equations - Birkhäuser-Verlag, 2001, 6(2006), 3 vom: Aug., Seite 419-432 |
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| Übergeordnetes Werk: |
volume:6 ; year:2006 ; number:3 ; month:08 ; pages:419-432 |
| Links: |
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| DOI / URN: |
10.1007/s00028-006-0258-7 |
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OLC2062452055 |
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| 520 | |a Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. | ||
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| 650 | 4 | |a Inverse Function Theorem | |
| 650 | 4 | |a Close Graph Theorem | |
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10.1007/s00028-006-0258-7 doi (DE-627)OLC2062452055 (DE-He213)s00028-006-0258-7-p DE-627 ger DE-627 rakwb eng 510 VZ Aubin, Jean-Pierre verfasserin aut A viability approach to the inverse set-valued map theorem 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. Differential Inclusion Viability Approach Closed Convex Cone Inverse Function Theorem Close Graph Theorem Enthalten in Journal of evolution equations Birkhäuser-Verlag, 2001 6(2006), 3 vom: Aug., Seite 419-432 (DE-627)340078006 (DE-600)2065368-2 (DE-576)09660719X 1424-3199 nnns volume:6 year:2006 number:3 month:08 pages:419-432 https://doi.org/10.1007/s00028-006-0258-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4325 AR 6 2006 3 08 419-432 |
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10.1007/s00028-006-0258-7 doi (DE-627)OLC2062452055 (DE-He213)s00028-006-0258-7-p DE-627 ger DE-627 rakwb eng 510 VZ Aubin, Jean-Pierre verfasserin aut A viability approach to the inverse set-valued map theorem 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. Differential Inclusion Viability Approach Closed Convex Cone Inverse Function Theorem Close Graph Theorem Enthalten in Journal of evolution equations Birkhäuser-Verlag, 2001 6(2006), 3 vom: Aug., Seite 419-432 (DE-627)340078006 (DE-600)2065368-2 (DE-576)09660719X 1424-3199 nnns volume:6 year:2006 number:3 month:08 pages:419-432 https://doi.org/10.1007/s00028-006-0258-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4325 AR 6 2006 3 08 419-432 |
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10.1007/s00028-006-0258-7 doi (DE-627)OLC2062452055 (DE-He213)s00028-006-0258-7-p DE-627 ger DE-627 rakwb eng 510 VZ Aubin, Jean-Pierre verfasserin aut A viability approach to the inverse set-valued map theorem 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. Differential Inclusion Viability Approach Closed Convex Cone Inverse Function Theorem Close Graph Theorem Enthalten in Journal of evolution equations Birkhäuser-Verlag, 2001 6(2006), 3 vom: Aug., Seite 419-432 (DE-627)340078006 (DE-600)2065368-2 (DE-576)09660719X 1424-3199 nnns volume:6 year:2006 number:3 month:08 pages:419-432 https://doi.org/10.1007/s00028-006-0258-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4325 AR 6 2006 3 08 419-432 |
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10.1007/s00028-006-0258-7 doi (DE-627)OLC2062452055 (DE-He213)s00028-006-0258-7-p DE-627 ger DE-627 rakwb eng 510 VZ Aubin, Jean-Pierre verfasserin aut A viability approach to the inverse set-valued map theorem 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. Differential Inclusion Viability Approach Closed Convex Cone Inverse Function Theorem Close Graph Theorem Enthalten in Journal of evolution equations Birkhäuser-Verlag, 2001 6(2006), 3 vom: Aug., Seite 419-432 (DE-627)340078006 (DE-600)2065368-2 (DE-576)09660719X 1424-3199 nnns volume:6 year:2006 number:3 month:08 pages:419-432 https://doi.org/10.1007/s00028-006-0258-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4325 AR 6 2006 3 08 419-432 |
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10.1007/s00028-006-0258-7 doi (DE-627)OLC2062452055 (DE-He213)s00028-006-0258-7-p DE-627 ger DE-627 rakwb eng 510 VZ Aubin, Jean-Pierre verfasserin aut A viability approach to the inverse set-valued map theorem 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. Differential Inclusion Viability Approach Closed Convex Cone Inverse Function Theorem Close Graph Theorem Enthalten in Journal of evolution equations Birkhäuser-Verlag, 2001 6(2006), 3 vom: Aug., Seite 419-432 (DE-627)340078006 (DE-600)2065368-2 (DE-576)09660719X 1424-3199 nnns volume:6 year:2006 number:3 month:08 pages:419-432 https://doi.org/10.1007/s00028-006-0258-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4325 AR 6 2006 3 08 419-432 |
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Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. © Birkhäuser Verlag, Basel 2006 |
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Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. © Birkhäuser Verlag, Basel 2006 |
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Abstract. The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. © Birkhäuser Verlag, Basel 2006 |
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