Approximation of Continuous Functions by de La Vallee-Poussin Operators - Rukasov, V. I.; Silin, E. S.; Рукасов, В. И.; Силин, Е. С.; Рукасов, В. И.; Силин, Е. С. (Institute of Mathematics, NAS of Ukraine, 2005)
For $σ → ∞$, we study the asymptotic behavior of upper bounds of deviations of functions blonding to the classes $\widehat{C}_{∞}^{\overline{Ψ}}$ and $\widehat{C}^{\overline{Ψ}} H_{ω}$ 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 $\widehat{C}_{∞}^{\overline{Ψ}}$ and $\widehat{C}^{\overline{Ψ}} H_{ω}$.