Voitenko S. Investigation of approximative characteristics of classes of functions of one and several variables

Asymptotic equations are found for the least upper bound deviations of the Rogosinski operators on the classes {widehat C^{bar psi}_{infty}} of continuous functions in a uniform metric. Exact order estimates for the best M-term trigonometric approximations of the classes B^{Omega}_{p,theta} in the space L_q, 1 le p, q le infty, are received.The order estimates for the best M-term orthogonal trigonometric approximations of the classes B^{Omega}_{p,theta} in the space L_q, 1 le p, q le infty, (p,q) notin {(1, 1), (infty, infty)} and Greedy algoritms of the classes B^{Omega}_{p,theta} in the space L_q, 1 le p, q le infty, are obtained.