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Degrees of the approximations by some special matrix means of conjugate Fourier series

Kranz Radosława, Rzepka Aleksandra, Sylwestrzak-Maślanka Ewa

Demonstratio Mathematica

2019

Vol. 52, nr 1

116--129

In this paper we will present the pointwise and normwise estimations of the deviations considered by W. Łenski, B. Szal, [Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24] and S. Saini, U. Singh, [Boll. Unione Mat. Ital., 2016, 9, 495-504] under general assumptions on the class considered sequences defining the method of the summability. We show that the obtained estimations are the best possible for some subclasses of Lp by constructing the suitable type of functions.

On the approximation of integrable functions by some special matrix means of Fourier series

Kranz R., Rzepka A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

351--359

The results concerninig pointwise approximation and product of summability methods corresponding to the theorems of Xh. Z. Krasniqi [Poincare J. Anal. Appl., 2014, 1, 1-8] and W. Łenski and B. Szal [Math. Slovaca, 2016, 66(6), 1-12] are generalized. Some special cases are also formulated as corollaries.

On the approximation of functions from Lp by some special matrix means of Fourier series

Kranz R., Rzepka A.

Fasciculi Mathematici

2015

Nr 55

81--90

The results corresponding to some theorems of S. Lal [Appl. Math. and Comput. 209 (2009), 346-350] and the results of W. Lenski and B. Szal [Banach Center Publ., 95, (2011), 339-351] are shown. The better degrees of pointwise approximation than these in mentioned papers by another assumptions on summability methods for considered functions are obtained. From presented pointwise results the estimation on norm approximation are derived. Some special cases as corollaries are also formulated.

On the approximation of conjugate functions from Lp by some special matrix means of conjugate Fourier series

Krantz R., Rzepka A.

Commentationes Mathematicae

2014

Vol 54, No. 2

191--202

The results corresponding to some theorems of W. Łenski and B. Szal are shown. From the presented pointwise results the estimates on norm approximation are derived. Some special cases as corollaries are also formulated.

Pointwise strong and very strong approximation by matrix means of Fourier series

Łenski W., Szal B.

Commentationes Mathematicae

2008

Vol. 48, [Z] 2

177-198

We generalize and extend the some results of the paper [6]. Considering a wider class of function and more general means we obtain the results of the V. Totik type [8, 9].