Voitovych V. Approximation of classes of (psi,beta)-differentiable functions by interpolation analogous Vallee Poussin sums

For a wide range of generating successions psi(k), covering cases of infinitely differential, analytic and entire functions, the solution of Kolmogorov-Nikolskyi problem is found by the approximation by the interpolation analogs of de la Valle'e Poussin sums on C^psi_beta,s, 1 leq s leq infty and C^psi_beta H_omega classes. The inequalities of Lebesgue type for the approximation by the interpolation analogs of de la Valle'e Poussin sums on sets C^psi_overlinebeta L_s, 1 leq s leq infty and C^psi_overlinebeta C are established, where successions psi(k) defining these classes fall to zero swifter than the arbitrary geometric progression.