The pointwise estimates of the deviation Tn,Af(⋅)−f(⋅) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f , with application of the rth differences of the entries of A , are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.
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We extend the results of Xh. Z. Krasniqi [Acta Comment. Univ. Tartu. Math., 2013, 17, 89-101] and the authors [Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24] to the case of 2π/r-periodic functions. More over, as a measure of approximation r-differences of the entries are used.
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The pointwise estimates of the deviations (…) and (…) in terms of moduli of continuity (…) and (…) are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal [3, Theorem 1, p. 437].
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We show the results corresponding to theorems of S. Lai [Appl. Math. Comput., 209 (2009) 346-350] on the rate of approximation of functions from the generalized integral Lipschitz classes by matrix summability means of their Fourier series as well as to the authors theorems [Acta Comment. Univ. Tartu. Math., 13 (2009), 11-24] also on such approximations.
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In this paper, the rates of approximation of Lebesgue-integrable functions by the Taylor means of their Fourier series are estimated by the characteristics created by the relation defining the Lebesgue-type points. Some corollaries for Lipschitz functions are also derived.
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