Musiienko A. Inequalities of Lebegs type for de la Vallee Poussin sums upon sets of (psi,beta)-differentiable functions

In the number of cases inequalities of Lebesque type for de la Vallee Poussin sums upon sets of(psi,beta)-differentiable functions C_beta^psi C, C_beta^psi L_s, 1leq sleqinfty and L^psi_beta L_1, where estimates for rates of deviations of de la Vallee Poussin sums from functions are represented in terms of values of best approximations of their (psi,beta)-derivatives in C, L_s and L_1 spaces, respectively, are obtained. Asymptotical equalities for precise upper borders of uniform approximations by de la Vallee Poussin sums upon classes of 2pi-periodical functions, with psi(k) sequence satisfying d'Alembert condition, are obtained.