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 Probl. Anal. Issues Anal., 2021, Volume 10(28), Issue 1, Pages 87–100 (Mi pa318)

Modified modulus of smoothness and approximation in weighted Lorentz spaces by Borel and Euler means

S. S. Volosivets

Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia

Abstract: Using one-sided Steklov means, we introduce a new modulus of smoothness in weighted Lorentz spaces. The direct and inverse approximation theorem for this modulus of smoothness are proved. Also, we estimate the rate of approximation by the Borel and Euler means in weighted Lorentz spaces.

Keywords: weighted Lorentz spaces, direct and inverse approximation theorems, Borel means, Euler means.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation FSRR-2020-0006 Supported by the Ministry of science and education of the Russian Federation in the framework of the basic part of the scientific research state task, project FSRR-2020-0006.

DOI: https://doi.org/10.15393/j3.art.2021.8950

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Bibliographic databases:

UDC: 517.518.832, 517.518.235
MSC: 42A10, 42A24
Revised: 30.11.2020
Accepted:09.12.2020
Language:

Citation: S. S. Volosivets, “Modified modulus of smoothness and approximation in weighted Lorentz spaces by Borel and Euler means”, Probl. Anal. Issues Anal., 10(28):1 (2021), 87–100

Citation in format AMSBIB
\Bibitem{Vol21} \by S.~S.~Volosivets \paper Modified modulus of smoothness and approximation in weighted Lorentz spaces by Borel and Euler means \jour Probl. Anal. Issues Anal. \yr 2021 \vol 10(28) \issue 1 \pages 87--100 \mathnet{http://mi.mathnet.ru/pa318} \crossref{https://doi.org/10.15393/j3.art.2021.8950} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000621661400006}