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On summability of Fourier series by the repeated de la Vallée Poussin sums

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Abstract

Using the repeated de la Vallée Poussin sums, we have proved four theorems which show the upper bound of the repeated de la Vallée Poussin kernel, the convergence of Fourier series, the deviation between a continuous function and their repeated de la Vallée Poussin sums of partial sums of their Fourier series, and the degree of approximation of functions belonging to ordinary Lipschitz class.

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Acknowledgements

The author would like to thank the referees for their useful comments for the first version of this paper and especially for drawing attention us to the reference [22].

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  1. Faculty of Education, Department of Mathematics and Informatics, University of Prishtina “Hasan Prishtina”, Avenue “Mother Theresa” No. 5, Prishtinë, 10000, Republic of Kosovo

    Xhevat Zahir Krasniqi

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  1. Xhevat Zahir Krasniqi
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Correspondence to Xhevat Zahir Krasniqi.

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Communicated by Samy Ponnusamy.

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Krasniqi, X.Z. On summability of Fourier series by the repeated de la Vallée Poussin sums. J Anal 29, 1327–1337 (2021). https://doi.org/10.1007/s41478-021-00313-w

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