Generalized Lagrange Theorem
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913186203041792 |
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| author | Zając, Karolina |
| author_facet | Zając, Karolina |
| contents | The present paper is devoted to possible generalizations of the classic Lagrange Mean Value Theorem. We consider a real-valued function of several variables that is only assumed to be continuous. The main concept is to replace the notion of the derivative by the so called bisequential tangent cone. We first prove Rolle and Lagrange type results and then we turn to comparing this cone with the Clarke subdifferential in the case of a Lipschitz function. We also investigate an approach using normal cones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09237 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Lagrange Theorem Zając, Karolina Classical Analysis and ODEs Optimization and Control 26A24 The present paper is devoted to possible generalizations of the classic Lagrange Mean Value Theorem. We consider a real-valued function of several variables that is only assumed to be continuous. The main concept is to replace the notion of the derivative by the so called bisequential tangent cone. We first prove Rolle and Lagrange type results and then we turn to comparing this cone with the Clarke subdifferential in the case of a Lipschitz function. We also investigate an approach using normal cones. |
| title | Generalized Lagrange Theorem |
| topic | Classical Analysis and ODEs Optimization and Control 26A24 |
| url | https://arxiv.org/abs/2303.09237 |