Approximation of Continuous Functions by de La Vallee-Poussin Operators
For $\sigma \rightarrow \infty$, we study the asymptotic behavior of upper bounds of deviations of functions blonding to the classes $\widehat{C}_{\infty}^{\overline{\Psi}}$ and $\widehat{C}^{\overline{\Psi}} H_{\omega}$ from the so-called Vallee Poussin operators. We find asymptotic equalities th...
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| Date: | 2005 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3590 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | For $\sigma \rightarrow \infty$, we study the asymptotic behavior of upper bounds of deviations of functions blonding to the classes
$\widehat{C}_{\infty}^{\overline{\Psi}}$ and $\widehat{C}^{\overline{\Psi}} H_{\omega}$ from the so-called Vallee Poussin operators.
We find asymptotic equalities that, in some important cases, guarantee the solution of the Kolmogorov - Nikol's'kyi problem for the Vallee Poussin operators on the classes
$\widehat{C}_{\infty}^{\overline{\Psi}}$ and $\widehat{C}^{\overline{\Psi}} H_{\omega}$.
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