Approximation of the Classes \(C^{{\bar \psi }} H_{\omega }\) by de la Vallée-Poussin Sums

We investigate the problem of the approximation of the classes \(C^{{\bar \psi }} H_{\omega }\) introduced by Stepanets in 1996 by the de la Valee-Poussin sums. We obtain asymptotic equalities that give a solution of the Kolmogorov–Nikol'skii problem for the de la Valee-Poussin sums on the classes \(C^{{\bar \psi }} H_{\omega }\) in several important cases.