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NEGATIVE THEOREM FOR LP,0 | ||
| Journal of Kufa for Mathematics and Computer | ||
| Article 1, Volume 4, Issue 3, 2017, Pages 1-3 | ||
| Author | ||
| GHAZI ABDULLAH | ||
| Abstract | ||
| 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 ́ )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f ́ )〗_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 ́ )〗_p is the degree of the best Lp approximation of the function f ́ by algebraic polynomial of degree not exceeding n. | ||
| Keywords | ||
| monotone approximation; algebraic polynomial; best approximation | ||
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