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

Authors

  • O.V. Fedunyk-Yaremchuk Lesya Ukrainka Volyn National University, 13 Voli ave., 43025, Lutsk, Ukraine
  • S.B. Hembars'ka Lesya Ukrainka Volyn National University, 13 Voli ave., 43025, Lutsk, Ukraine
  • K.V. Solich Lesya Ukrainka Volyn National University, 13 Voli ave., 43025, Lutsk, Ukraine
https://doi.org/10.15330/cmp.15.2.468-481

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∞,θBΩ∞,θ of periodic functions of several variables with a given function Ω(t)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∞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.

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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.

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