Approximation of Continuous Functions by de La Vallee-Poussin Operators

摘要

We study the asymptotic (as σ → ∞) behavior of upper bounds of the deviations of functions belonging to the classes C_∞~ψ and C~ψH_ω 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 C_∞~ψ and C~ψH_ω.