An Extension of the Carathéodory Differentiability to Set-Valued Maps
This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/5529796 |
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| _version_ | 1832550072183685120 |
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| author | Pedro Hurtado Alexander Leones M. Martelo J. B. Moreno |
| author_facet | Pedro Hurtado Alexander Leones M. Martelo J. B. Moreno |
| author_sort | Pedro Hurtado |
| collection | DOAJ |
| description | This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-differentiability for multifunctions. Finally, we tackle the study of the relation among the Fréchet differentiability, Hukuhara differentiability, and CH-differentiability. |
| format | Article |
| id | doaj-art-6665bcd86e2d4572a3d67fed4e2f0447 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6665bcd86e2d4572a3d67fed4e2f04472025-02-03T06:07:43ZengWileyAbstract and Applied Analysis1085-33751687-04092021-01-01202110.1155/2021/55297965529796An Extension of the Carathéodory Differentiability to Set-Valued MapsPedro Hurtado0Alexander Leones1M. Martelo2J. B. Moreno3Facultad de Ingenierías, Corporación Universitaria Remington, Calle 51, N 51-27 Medellín-Antioquia, ColombiaFacultad de Ingenierías, Corporación Universitaria Remington, Calle 51, N 51-27 Medellín-Antioquia, ColombiaProgram of Mathematics, Universidade Federal Fluminense, Niteroi, BrazilFacultad de Ingenierías, Corporación Universitaria Remington, Calle 51, N 51-27 Medellín-Antioquia, ColombiaThis paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-differentiability for multifunctions. Finally, we tackle the study of the relation among the Fréchet differentiability, Hukuhara differentiability, and CH-differentiability.http://dx.doi.org/10.1155/2021/5529796 |
| spellingShingle | Pedro Hurtado Alexander Leones M. Martelo J. B. Moreno An Extension of the Carathéodory Differentiability to Set-Valued Maps Abstract and Applied Analysis |
| title | An Extension of the Carathéodory Differentiability to Set-Valued Maps |
| title_full | An Extension of the Carathéodory Differentiability to Set-Valued Maps |
| title_fullStr | An Extension of the Carathéodory Differentiability to Set-Valued Maps |
| title_full_unstemmed | An Extension of the Carathéodory Differentiability to Set-Valued Maps |
| title_short | An Extension of the Carathéodory Differentiability to Set-Valued Maps |
| title_sort | extension of the caratheodory differentiability to set valued maps |
| url | http://dx.doi.org/10.1155/2021/5529796 |
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