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1
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On the degree of strong approximation of integrable functions in Stepanov sense

100%
Łenski W., Szal B.
Banach Center Publications
|
2014
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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.
2
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Lebesgue type points in strong (C,α) approximation of Fourier series

100%
Łenski W., Roszak B.
Banach Center Publications
|
2011
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tom 92
|
nr 1
219-235
EN
We present an estimation of the $H_{k₀,k_{r}}^{q,α}f$ and $H_{λ,u}^{ϕ,α}f$ means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.
3
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Approximation of functions from \(L^p(\omega)_\beta\) by linear operators of their Fourier series

100%
Łenski W., Szal B.
Commentationes Mathematicae
|
2011
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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.
4
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Pointwise strong and very strong approximation by matrix means of Fourier series

100%
Łenski W., Szal B.
Commentationes Mathematicae
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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].
5
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Approximation of functions from $L^{p}(ω)_{β}$ by general linear operators of their Fourier series

100%
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].
6
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On the approximation of functions by matrix means in the generalized Hölder metric

100%
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.
7
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On the pointwise strong approximation by (C,1)(E,1) means

100%
Łenski W., Roszak B.
Banach Center Publications
|
2008
|
tom 79
|
nr 1
113-117
EN
We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function $f ∈ L_{2π}$ as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.
8
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Pointwise strong approximation of almost periodic functions

81%
Kranz R., Łenski W., Szal B.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2016
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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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