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1
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On the uniform convergence of weighted trigonometric series

100%
Szal B.
Banach Center Publications
|
2011
|
tom 92
|
nr 1
339-350
EN
In the present paper we consider a new class of sequences called GM(β,r), which is the generalization of a class defined by Tikhonov in [15]. We obtain sufficient and necessary conditions for uniform convergence of weighted trigonometric series with (β,r)-general monotone coefficients.
2
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On the rate of summability by matrix means in the generalized Hölder metric

100%
Szal B.
Banach Center Publications
|
2011
|
tom 95
|
nr 1
359-368
EN
We will generalize and improve the results of T. Singh [Publ. Math. Debrecen 40 (1992), 261-271] obtaining the L. Leindler type estimates from [Acta Math. Hungar. 104 (2004), 105-113].
3
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A note on the MRBSVS class and its application to the uniform convergence and boundedness of sine series

100%
Szal B.
Commentationes Mathematicae
|
2009
|
tom 49
|
nr 1
EN
A new class of \(\gamma\) rest bounded second variation sequences is defined. Some relationships between classes of considered sequences are proved. The results of Leindler [3] and author [8] are extended to our new class.
4
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On the approximation by Euler, Borel and Taylor means in enlarged Hölder classes

100%
Szal B.
Banach Center Publications
|
2008
|
tom 79
|
nr 1
203-211
EN
We generalize and improve in some cases the results of Mahapatra and Chandra [7]. As a measure of Hölder norm approximation, generalized modulus-type functions are used.
5
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A note on the uniform convergence and boundedness of a generalized class of sine series

100%
Szal B.
Commentationes Mathematicae
|
2008
|
tom 48
|
nr 1
EN
In this paper we essentially extend the Leindler’s results concerning the uniform convergence and boundedness of a certain class of sine series.
6
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On the degree of strong approximation of integrable functions in Stepanov sense

64%
Łenski W., Szal B.
Banach Center Publications
|
2014
|
tom 102
|
nr 1
169-179
EN
Considering the class of almost periodic functions integrable in the Stepanov sense we extend and generalize certain results of the first author, as well as of L. Leindler and P. Chandra.
7
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Approximation of functions from $L^{p}(ω̃)_{β}$ by linear operators of conjugate Fourier series

64%
Łenski W., Szal B.
Banach Center Publications
|
2011
|
tom 92
|
nr 1
237-247
EN
We show the results corresponding to some theorems of S. Lal and H. K. Nigam [Int. J. Math. Math. Sci. 27 (2001), 555-563] on the norm and pointwise approximation of conjugate functions and to the results of the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] also on such approximations.
8
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Approximation of functions from \(L^p(\omega)_\beta\) by linear operators of their Fourier series

64%
Łenski W., Szal B.
Commentationes Mathematicae
|
2011
|
tom 51
|
nr 2
EN
We show the results corresponding to theorems of S. Lal [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.
9
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Pointwise strong and very strong approximation by matrix means of Fourier series

64%
Łenski W., Szal B.
Commentationes Mathematicae
|
2008
|
tom 48
|
nr 2
EN
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].
10
Content available remote

Approximation of functions from $L^{p}(ω)_{β}$ by general linear operators of their Fourier series

64%
Łenski W., Szal B.
Banach Center Publications
|
2011
|
tom 95
|
nr 1
339-351
EN
We show the general and precise conditions on the functions and modulus of continuity as well as on the entries of matrices generating the summability means and give the rates of approximation of functions from the generalized integral Lipschitz classes by double matrix means of their Fourier series. Consequently, we give some results on norm approximation. Thus we essentially extend and improve our earlier results [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] and the result of S. Lal [Appl. Math. Comput. 209 (2009), 346-350].
11
Content available remote

On the approximation of functions by matrix means in the generalized Hölder metric

64%
Łenski W., Szal B.
Banach Center Publications
|
2008
|
tom 79
|
nr 1
119-129
EN
Under some assumptions on the matrix of a summability method, whose rows are sequences of bounded variation, we obtain a generalization and an improvement of some results of Xie-Hua Sun and L. Leindler.
12
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Pointwise strong approximation of almost periodic functions

52%
Kranz R., Łenski W., Szal B.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2016
|
tom 36
|
nr 1
45-63
EN
We consider the class GM(₂β) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.
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