Metrically differentiable set-valued functions and their local linear approximants
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916146649759744 |
|---|---|
| author | Mokhov, Alona Dyn, Nira Farkhi, Elza |
| author_facet | Mokhov, Alona Dyn, Nira Farkhi, Elza |
| contents | A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically differentiable set-valued function at a point is defined and studied. This local approximant may be regarded as a special realization of the set-valued Euler approximants of M.~S.~Nikolskii and the directives of Z.~Artstein. Error estimates for the local metric linear approximant are obtained. In particular, second order approximation is derived for a class of ``strongly'' metrically differentiable set-valued maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02858 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metrically differentiable set-valued functions and their local linear approximants Mokhov, Alona Dyn, Nira Farkhi, Elza Classical Analysis and ODEs A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically differentiable set-valued function at a point is defined and studied. This local approximant may be regarded as a special realization of the set-valued Euler approximants of M.~S.~Nikolskii and the directives of Z.~Artstein. Error estimates for the local metric linear approximant are obtained. In particular, second order approximation is derived for a class of ``strongly'' metrically differentiable set-valued maps. |
| title | Metrically differentiable set-valued functions and their local linear approximants |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.02858 |