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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Faculty of Computer Science and Mathematics, University of Kufa
2017-12-01
|
| Series: | Journal of Kufa for Mathematics and Computer |
| Subjects: | |
| Online Access: | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/2102 |
| Summary: | 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. |
|---|---|
| ISSN: | 2076-1171 2518-0010 |