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

Xhevat Z. Krasniqi; Xhevat Z. Krasniqi

doi:10.3934/math.2024166

AIMS Mathematics

2024, Volume 9, Issue 2: 3386-3398. doi: 10.3934/math.2024166

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Research article

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

Xhevat Z. Krasniqi ^,

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

Received: 27 September 2023 Revised: 26 November 2023 Accepted: 28 November 2023 Published: 05 January 2024
MSC : 26A16, 41A25, 42A50

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.
- degree of approximation,
- $ q $-Singular integrals,
- modulus of continuity,
- generalized Hölder class,
- generalized Minkowski inequality
Citation: Xhevat Z. Krasniqi. Approximation of functions in a certain Banach space by some generalized singular integrals[J]. AIMS Mathematics, 2024, 9(2): 3386-3398. doi: 10.3934/math.2024166

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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.

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