APPROXIMATION OF INTEGRABLE FUNCTIONS BY GENERALIZED DE LA VALLÉE POUSSIN MEANS OF THE POSITIVE ORDER

Xhevat Z. Krasniqi; Włodzimierz Łenski; Bogdan Szal

doi:10.11948/20210067

2022 Volume 12 Issue 1

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Xhevat Z. Krasniqi, Włodzimierz Łenski, Bogdan Szal. APPROXIMATION OF INTEGRABLE FUNCTIONS BY GENERALIZED DE LA VALLÉE POUSSIN MEANS OF THE POSITIVE ORDER[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 106-124. doi: 10.11948/20210067

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Xhevat Z. Krasniqi, Włodzimierz Łenski, Bogdan Szal. APPROXIMATION OF INTEGRABLE FUNCTIONS BY GENERALIZED DE LA VALLÉE POUSSIN MEANS OF THE POSITIVE ORDER[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 106-124. doi: 10.11948/20210067

APPROXIMATION OF INTEGRABLE FUNCTIONS BY GENERALIZED DE LA VALLÉE POUSSIN MEANS OF THE POSITIVE ORDER

1.
University of Prishtina "Hasan Prishtina", Faculty of Education, Department of Mathematics and Informatics, Avenue "Mother Theresa", Prishtinë 10000, Republic of Kosova
2.
University of Zielona Góra, Faculty of Mathematics, Computer Science and Econometrics, 65-516 Zielona Góra, ul. Szafrana 4a, Poland

Corresponding author: Email: xhevat.krasniqi@uni-pr.edu (Xhevat Z. Krasniqi)

Abstract

Abstract

In this paper several results pertaining to the pointwise and normwise approximation of integrable functions by generalized de la Vallée Poussin means of positive order are presented. The pointwise estimates of the considered deviation in terms of pointwise moduli of continuity based on the Lebesgue points and points of differentiability of indefinite integral are obtained. Some results of L. Leindler and the second author are generalized.
- Rate of approximation /
- summability of Fourier series /
- de la Vallée-Poussin mean /
- monotone sequence
MSC: 42A10, 42A24

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References

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