Best uniform approximation of semi-Lipschitz functions by extensions
In this paper we consider the problem of best uniform approximation of a real valued semi-Lipschitz function \(F\) defined on an asymmetric metric space \((X,d),\) by the elements of the set \(\mathcal{E}_{d}(\left. F\right\vert _{Y})\) of all extensions of \(\left.F\right\vert _{Y}\) \((Y\subset X)...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
2007-08-01
|
| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/864 |
| _version_ | 1828542654588125184 |
|---|---|
| author | Costică Mustăţa |
| author_facet | Costică Mustăţa |
| author_sort | Costică Mustăţa |
| collection | DOAJ |
| description | In this paper we consider the problem of best uniform approximation of a real valued semi-Lipschitz function \(F\) defined on an asymmetric metric space \((X,d),\) by the elements of the set \(\mathcal{E}_{d}(\left. F\right\vert _{Y})\) of all extensions of \(\left.F\right\vert _{Y}\) \((Y\subset X),\) preserving the smallest semi-Lipschitz constant. It is proved that this problem has always at least a solution, if \((X,d)\) is \((d,\overline{d})\)-sequentially compact, or of finite diameter. |
| first_indexed | 2024-12-12T02:00:51Z |
| format | Article |
| id | doaj.art-468a5a2eba514ed18ea92e7745108785 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-12T02:00:51Z |
| publishDate | 2007-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-468a5a2eba514ed18ea92e77451087852022-12-22T00:42:11ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2007-08-01362Best uniform approximation of semi-Lipschitz functions by extensionsCostică Mustăţa0Tiberiu Popoviciu Institute of Numerical Analysis, Romanian AcademyIn this paper we consider the problem of best uniform approximation of a real valued semi-Lipschitz function \(F\) defined on an asymmetric metric space \((X,d),\) by the elements of the set \(\mathcal{E}_{d}(\left. F\right\vert _{Y})\) of all extensions of \(\left.F\right\vert _{Y}\) \((Y\subset X),\) preserving the smallest semi-Lipschitz constant. It is proved that this problem has always at least a solution, if \((X,d)\) is \((d,\overline{d})\)-sequentially compact, or of finite diameter.https://www.ictp.acad.ro/jnaat/journal/article/view/864semi-Lipschitz functionsuniform approximationextensions of semi-Lipschitz functions |
| spellingShingle | Costică Mustăţa Best uniform approximation of semi-Lipschitz functions by extensions Journal of Numerical Analysis and Approximation Theory semi-Lipschitz functions uniform approximation extensions of semi-Lipschitz functions |
| title | Best uniform approximation of semi-Lipschitz functions by extensions |
| title_full | Best uniform approximation of semi-Lipschitz functions by extensions |
| title_fullStr | Best uniform approximation of semi-Lipschitz functions by extensions |
| title_full_unstemmed | Best uniform approximation of semi-Lipschitz functions by extensions |
| title_short | Best uniform approximation of semi-Lipschitz functions by extensions |
| title_sort | best uniform approximation of semi lipschitz functions by extensions |
| topic | semi-Lipschitz functions uniform approximation extensions of semi-Lipschitz functions |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/864 |
| work_keys_str_mv | AT costicamustata bestuniformapproximationofsemilipschitzfunctionsbyextensions |