Abstract
A sufficient condition for the order of approximation of a continuous 2π periodic function with a given majorant for the modulus of continuity by the [F, dn] means of its Fourier series to be of Jackson order is obtained. This sufficient condition is shown to be not enough for the order of approximation by partial sums of their Fourier series to be of Jackson order. The error estimate is shown to be the best possible.
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References
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Settu, S.A. Approximation of continuous functions by generalized karamata means. Approx. Theory & its Appl. 10, 88–98 (1994). https://doi.org/10.1007/BF02836302
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DOI: https://doi.org/10.1007/BF02836302