Approximation of Poisson integrals by r-repeated de la Vallee Poussin sums

The paper investigates the approximation properties of linear means of Fourier series generated by repeated application of the de la Vallée Poussin summation method. Asymptotic formulas for the exact upper bounds of deviations of the r-repeated de la Vallée Poussin means on the classes of Poisson integrals of functions with bounded generalized derivatives are obtained. The derived relations, under certain conditions, represent asymptotically exact equalities.