NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION
For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: (2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f Ì )〗_p, where 〖E_(n+1)^1 (f...
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| Format: | Article |
| Language: | English |
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Faculty of Computer Science and Mathematics, University of Kufa
2017-12-01
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| Series: | Journal of Kufa for Mathematics and Computer |
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| Online Access: | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/2102 |
| _version_ | 1797267007960252416 |
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| author | GHAZI ABDULLAH Madlol |
| author_facet | GHAZI ABDULLAH Madlol |
| author_sort | GHAZI ABDULLAH Madlol |
| collection | DOAJ |
| description | For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship:
(2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f Ì )〗_p,
where 〖E_(n+1)^1 (f)〗_p is the degree of the best Lp monotone approximation of the function f by algebraic polynomial of degree not exceeding n+1. 〖E_n (f Ì )〗_p is the degree of the best Lp approximation of the function f Ì by algebraic polynomial of degree not exceeding n. |
| first_indexed | 2024-04-25T01:09:45Z |
| format | Article |
| id | doaj.art-cab02ac2e03548eb89a3dc6b23327538 |
| institution | Directory Open Access Journal |
| issn | 2076-1171 2518-0010 |
| language | English |
| last_indexed | 2024-04-25T01:09:45Z |
| publishDate | 2017-12-01 |
| publisher | Faculty of Computer Science and Mathematics, University of Kufa |
| record_format | Article |
| series | Journal of Kufa for Mathematics and Computer |
| spelling | doaj.art-cab02ac2e03548eb89a3dc6b233275382024-03-10T10:27:42ZengFaculty of Computer Science and Mathematics, University of KufaJournal of Kufa for Mathematics and Computer2076-11712518-00102017-12-014310.31642/JoKMC/2018/040301NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATIONGHAZI ABDULLAH Madlol0UNIVERSITY OF BABYLONFor a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: (2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f Ì )〗_p, where 〖E_(n+1)^1 (f)〗_p is the degree of the best Lp monotone approximation of the function f by algebraic polynomial of degree not exceeding n+1. 〖E_n (f Ì )〗_p is the degree of the best Lp approximation of the function f Ì by algebraic polynomial of degree not exceeding n.https://journal.uokufa.edu.iq/index.php/jkmc/article/view/2102Monotone approximation algebraic polynomial best approximation. |
| spellingShingle | GHAZI ABDULLAH Madlol NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION Journal of Kufa for Mathematics and Computer Monotone approximation algebraic polynomial best approximation. |
| title | NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION |
| title_full | NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION |
| title_fullStr | NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION |
| title_full_unstemmed | NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION |
| title_short | NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION |
| title_sort | negative theorem for lp 0 p 1 monotone approximation |
| topic | Monotone approximation algebraic polynomial best approximation. |
| url | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/2102 |
| work_keys_str_mv | AT ghaziabdullahmadlol negativetheoremforlp0p1monotoneapproximation |