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

## Keywords:

mixed modulus of continuity, Bari-Stechkin condition, Nikol'skii-Besov-type class, linear operator, Vallée Poussin kernel, Fejér kernel### 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.

*Carpathian Math. Publ.*

**2023**,

*15*, 468-481.