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
Published online:
2023-12-05
Abstract
We obtain the exact-order estimates of approximation of the Nikol'skii-Besov-type classes BΩ∞,θ of periodic functions of several variables with a given function Ω(t) of a special form by using linear operators satisfying certain conditions. The approximation error is estimated in the metric of the space L∞. 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.
How to Cite
(1)
Fedunyk-Yaremchuk, O.; Hembars'ka, S.; Solich, K. Approximation of Classes of Periodic Functions of Several Variables With Given Majorant of Mixed Moduli of Continuity. Carpathian Math. Publ. 2023, 15, 468-481.