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Research Article | Open Access

Approximation of functions in a certain Banach space by some generalized singular integrals

Department of Teaching Mathematics, Faculty of Education, University of Prishtina "Hasan Prishtina", Avenue "Mother Theresa" no. 5, Prishtina 10000, Republic of Kosovo
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Abstract

We introduced the q-Picard, the q-Picard-Cauchy, the q-Gauss-Weierstrass, and the q-truncated Picard singular integrals. Using the last three mentioned integrals, the orders of approximation for functions from a generalized Hölder space were determined, both in the L p -norm and in the generalized Hölder-norm.

Keywords

degree of approximationq-Singular integralsmodulus of continuitygeneralized Hölder classgeneralized Minkowski inequality
CLC number: 26A16, 41A25, 42A50

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 3386-3398
DOI: 10.3934/math.2024166

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Cite this article:
Krasniqi XZ. Approximation of functions in a certain Banach space by some generalized singular integrals. AIMS Mathematics, 2024, 9(2): 3386-3398. https://doi.org/10.3934/math.2024166

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Received: 27 September 2023
Revised: 26 November 2023
Accepted: 28 November 2023
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)