Approximation of certain bivariate functions by almost Euler means of double Fourier series

In this paper, we study the degree of approximation of 2π-periodic functions of two variables, defined on [Formula: see text] and belonging to certain Lipschitz classes, by means of almost Euler summability of their Fourier series. The degree of approximation obtained in this way depends on the modu...

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Detalles Bibliográficos
Autores principales: Rathore, Arti, Singh, Uaday
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5902535/
https://www.ncbi.nlm.nih.gov/pubmed/29706744
http://dx.doi.org/10.1186/s13660-018-1676-0
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author Rathore, Arti
Singh, Uaday
author_facet Rathore, Arti
Singh, Uaday
author_sort Rathore, Arti
collection PubMed
description In this paper, we study the degree of approximation of 2π-periodic functions of two variables, defined on [Formula: see text] and belonging to certain Lipschitz classes, by means of almost Euler summability of their Fourier series. The degree of approximation obtained in this way depends on the modulus of continuity associated with the functions. We also derive some corollaries from our theorems.
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spelling pubmed-59025352018-04-24 Approximation of certain bivariate functions by almost Euler means of double Fourier series Rathore, Arti Singh, Uaday J Inequal Appl Research In this paper, we study the degree of approximation of 2π-periodic functions of two variables, defined on [Formula: see text] and belonging to certain Lipschitz classes, by means of almost Euler summability of their Fourier series. The degree of approximation obtained in this way depends on the modulus of continuity associated with the functions. We also derive some corollaries from our theorems. Springer International Publishing 2018-04-16 2018 /pmc/articles/PMC5902535/ /pubmed/29706744 http://dx.doi.org/10.1186/s13660-018-1676-0 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Rathore, Arti
Singh, Uaday
Approximation of certain bivariate functions by almost Euler means of double Fourier series
title Approximation of certain bivariate functions by almost Euler means of double Fourier series
title_full Approximation of certain bivariate functions by almost Euler means of double Fourier series
title_fullStr Approximation of certain bivariate functions by almost Euler means of double Fourier series
title_full_unstemmed Approximation of certain bivariate functions by almost Euler means of double Fourier series
title_short Approximation of certain bivariate functions by almost Euler means of double Fourier series
title_sort approximation of certain bivariate functions by almost euler means of double fourier series
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5902535/
https://www.ncbi.nlm.nih.gov/pubmed/29706744
http://dx.doi.org/10.1186/s13660-018-1676-0
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