Ovsiy E. Approximation of classes of (psi,beta)-differentiable functions by linear methods

Asymptotic equalities are found for least upper bounds of deviations in the uniform metric of the generalized trigonometrical polynomials of a special mode on the classes C^{psi}_{beta,infty} and C^{psi}_{beta}H_omega. Asymptotic equalities for least upper bounds of approximations by the sums of de la Vall'{e}e Poussin in the uniform metric on the classes of 2pi-periodic functions C^psi_{bar{beta},s}, 1 leqslant s leqslant infty and C^psi_{bar{beta}}H_omega are discovered. Similar results are received in metrics of spaces L_s, 1 leqslant s leqslant infty, for the classes L^psi_{bar{beta},1} and in the metric L_1 for the сlasses L^psi_{bar{beta}}H_{omega_1}.