Approximation of classes of periodic functions of several variables with given majorant of mixed moduli of continuity

Abstract

We obtain the exact-order estimates of approximation of the Nikol'skii-Besov-type classes $B^{\Omega}_{\infty,\theta}$ of periodic functions of several variables with a given function $\Omega(t)$ of a special form by using linear operators satisfying certain conditions. The approximation error is estimated in the metric of the space $L_{\infty}$. The obtained estimates of the considered approximation characteristic, in addition to independent interest, can be used to establish the lower bounds of the orthowidths of the corresponding functional classes.