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Approximation of integrable functions by general linear matrix operators of their Fourier series

Mishra Vishnu Narayan, Łenski Włodzimierz, Szal Bogdan

Demonstratio Mathematica

2022

Vol. 55, nr 1

136--152

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.

Point wise approximation of 2π/r-periodic functions by matrix operators of their Fourier series with r-differences of the entries

Łenski W., Szal B.

Demonstratio Mathematica

2018

Vol. 51, nr 1

309--322

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.

Approximation of conjugate functions by general linear operators of their Fourier series at the Lebesgue points

Łenski W., Szal B.

Demonstratio Mathematica

2014

Vol. 47, nr 4

878--892

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].

Approximation of functions from IP {uj)p by linear operators of their Fourier series

Łenski W., Szal B.

Commentationes Mathematicae

2011

Vol. 51, [Z] 2

189-202

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.

On the pointwise approximation by Taylor means

Roszak B.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2001

[Z] 41

171-181

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.