Approximation of Analytic Periodic Functions by de la Vallée-Poussin Sums

Abstract

We investigate the approximation properties of the de la Vallée-Poussin sums on the classes $C_{\beta }^q H_{\omega }$ . We obtain asymptotic equalities that, in certain cases, guarantee the solvability of the Kolmogorov–Nikol'skii problem for the de la Vallée-Poussin sums on the classes $C_{\beta }^q H_{\omega }$