Asymptotic estimates of approximation of continuous periodic functions by the Fourier sums

Abstract

Asymptotic estimates, expressed in terms of the value of the modulus of continuity of $r$-th order ($r\geq 2$) at the point $t = \pi/n$ of a function $f\in C_{2\pi}$ or of the ($\psi,\beta$)-derivative of a function $f \in C_{\beta}^{\psi}C$, are established for the deviations of continuous periodic functions from their Fourier sums.