On the best approximation of certain classes of periodic functions by trigonometric polynomials

Abstract

We obtain the estimates for the best approximation in the uniform metric of the classes of $2\pi$-periodic functions whose $(\psi ,\beta )$-derivatives have a given majorant $\omega$ of the modulus of continuity. It is shown that the estimates obtained here are asymptotically exact under some natural conditions on the parameters $\psi ,$ $\omega$ and $\beta$ defining the classes