Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911719177060352 |
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| author | Jung, Kiyuob |
| author_facet | Jung, Kiyuob |
| contents | This paper introduces specular differentiation, which generalizes Gâteaux and Fréchet differentiation in normed vector spaces. We investigate its fundamental theoretical properties and establish weak forms of the Mean Value Theorem and Fermat's Theorem in the specular sense. Finally, we identify a distinguished element of the Fréchet subdifferential of a convex function through specular differentiation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10950 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems Jung, Kiyuob Optimization and Control Numerical Analysis Classical Analysis and ODEs 46G05, 46T20, 49J52 This paper introduces specular differentiation, which generalizes Gâteaux and Fréchet differentiation in normed vector spaces. We investigate its fundamental theoretical properties and establish weak forms of the Mean Value Theorem and Fermat's Theorem in the specular sense. Finally, we identify a distinguished element of the Fréchet subdifferential of a convex function through specular differentiation. |
| title | Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems |
| topic | Optimization and Control Numerical Analysis Classical Analysis and ODEs 46G05, 46T20, 49J52 |
| url | https://arxiv.org/abs/2601.10950 |