Approximation of classes $C_\infty ^{\bar \psi }$ by zygmund sumsby zygmund sums

Abstract

We consider the approximation of functions of the classes of $\bar \psi$ by Zygmund sums. In papticular, we present asymptotic equalities for the quantities $\varepsilon _n (C_\infty ^{\bar \psi } ;Z_n )_C$ under various conditions imposed on functions $ψ_1(·)$ and $ψ_2(·)$.