Approximation of Continuous Functions by de la Vallée-Poussin Operators

We study the asymptotic (as σ → ∞) behavior of upper bounds of the deviations of functions belonging to the classes \(\hat C_\infty ^{\bar \psi }\) and \(\hat C^{\bar \psi } H_\omega\) from the so-called de la Vallee-Poussin operators. We obtain asymptotic equalities that, in some important cases, give a solution of the Kolmogorov-Nikol’skii problem for the de la Vallee-Poussin operators on the classes \(\hat C_\infty ^{\bar \psi }\) and \(\hat C^{\bar \psi } H_\omega\).