Polynomial approximation with an exponential weight in [-1,1] (revisiting some of Lubinsky's results)
Revisiting the results in [7], [8], we consider the polynomial approximation on (—1,1) with the weight w(x) = e~(1 x ' , a > 0. We introduce new moduli of smoothness, equivalent to suitable K-functionals, and we prove the Jackson theorem, also in its weaker form. Moreover, we state a new Be...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2011
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| Sorozat: | Acta scientiarum mathematicarum
77 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16384 |
| Tartalmi kivonat: | Revisiting the results in [7], [8], we consider the polynomial approximation on (—1,1) with the weight w(x) = e~(1 x ' , a > 0. We introduce new moduli of smoothness, equivalent to suitable K-functionals, and we prove the Jackson theorem, also in its weaker form. Moreover, we state a new Bernstein inequality, which allows us to prove the Salem-Stechkin inequality. Finally, also the behaviour of the derivatives of the polynomials of best approximation is discussed. |
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| Terjedelem/Fizikai jellemzők: | 167-207 |
| ISSN: | 0001-6969 |