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

For upper bounds of the deviations of de la Vallee-Poussin sums taken over classes of functions that admit analytic extensions to a fixed strip of the complex plane, we obtain asymptotic equalities. In certain cases, these equalities give a solution of the corresponding Kolmogorov–Nikol'skii problem.