The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints
We consider the best $L_1$-approximation with interpolatory constraints for continuous mapping of a metric compact set $Q$ into a Banach space $X$. The unicity set’s criterion is obtained. This result generalizes the result for real functions that was proved by A. Pinkus and H. Strauss.
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Oles Honchar Dnipro National University
2024-12-01
|
| Series: | Researches in Mathematics |
| Subjects: | |
| Online Access: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/440/440 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841558889627123712 |
|---|---|
| author | M.Ye. Tkachenko V.M. Traktynska |
| author_facet | M.Ye. Tkachenko V.M. Traktynska |
| author_sort | M.Ye. Tkachenko |
| collection | DOAJ |
| description | We consider the best $L_1$-approximation with interpolatory constraints for continuous mapping of a metric compact set $Q$ into a Banach space $X$. The unicity set’s criterion is obtained. This result generalizes the result for real functions that was proved by A. Pinkus and H. Strauss. |
| format | Article |
| id | doaj-art-07846ecdff884f1f9f786c4d67c4a7d7 |
| institution | Kabale University |
| issn | 2664-4991 2664-5009 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Researches in Mathematics |
| spelling | doaj-art-07846ecdff884f1f9f786c4d67c4a7d72025-01-05T19:43:51ZengOles Honchar Dnipro National UniversityResearches in Mathematics2664-49912664-50092024-12-0132216216610.15421/242427The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraintsM.Ye. Tkachenko0https://orcid.org/0000-0002-9242-194XV.M. Traktynska1Oles Honchar Dnipro National UniversityOles Honchar Dnipro National UniversityWe consider the best $L_1$-approximation with interpolatory constraints for continuous mapping of a metric compact set $Q$ into a Banach space $X$. The unicity set’s criterion is obtained. This result generalizes the result for real functions that was proved by A. Pinkus and H. Strauss.https://vestnmath.dnu.dp.ua/index.php/rim/article/view/440/440$l_1$-approximationcontinuous banach-valued functionscriterion of the best $l_1$-approximant |
| spellingShingle | M.Ye. Tkachenko V.M. Traktynska The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints Researches in Mathematics $l_1$-approximation continuous banach-valued functions criterion of the best $l_1$-approximant |
| title | The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints |
| title_full | The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints |
| title_fullStr | The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints |
| title_full_unstemmed | The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints |
| title_short | The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints |
| title_sort | uniqueness of the best l 1 approximant of continuous banach valued functions under interpolatory constraints |
| topic | $l_1$-approximation continuous banach-valued functions criterion of the best $l_1$-approximant |
| url | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/440/440 |
| work_keys_str_mv | AT myetkachenko theuniquenessofthebestl1approximantofcontinuousbanachvaluedfunctionsunderinterpolatoryconstraints AT vmtraktynska theuniquenessofthebestl1approximantofcontinuousbanachvaluedfunctionsunderinterpolatoryconstraints AT myetkachenko uniquenessofthebestl1approximantofcontinuousbanachvaluedfunctionsunderinterpolatoryconstraints AT vmtraktynska uniquenessofthebestl1approximantofcontinuousbanachvaluedfunctionsunderinterpolatoryconstraints |