Approximation properties of some singular integral on the classes of functions defined by the modulus of continuity

I.V. Kal'chuk; Yu.I. Kharkevych

doi:10.15421/242603

Approximation properties of some singular integral on the classes of functions defined by the modulus of continuity

I.V. Kal'chuk (Lesya Ukrainka Volyn National University), https://orcid.org/0000-0001-8822-3716
Yu.I. Kharkevych (Lesya Ukrainka Volyn National University), https://orcid.org/0000-0002-8577-5096

Abstract

The paper investigates the asymptotic behavior of the exact upper bounds of deviations in the uniform metric of the Weierstrass integrals of functions belonging to the classes $$$W^rH_{\omega}$$$, generated by the modulus of continuity $$$\omega(t)$$$.

Keywords

modulus of continuity; asymptotic equality; Weierstrass integral; functional classes

MSC 2020

41A35; 41A60

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