2017
Том 69
№ 12

# Approximation of Continuous Functions by de La Vallee-Poussin Operators

Abstract

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 $\widehat{C}^{\overline{\Psi}} H_{\omega}$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 2, pp 271-281.

Citation Example: Rukasov V. I., Silin E. S. Approximation of Continuous Functions by de La Vallee-Poussin Operators // Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 230–238.

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