11 papers
Pointwise strong (H, Phi) approximation by Fourier series of L^{Psi} integrable functions
Wlodzimierz Lenski
We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized…
Pointwise summability of Fourier-Laguerre series of integrable functions
Maciej Kubiak, Wlodzimierz Lenski, Bogdan Szal
We present an approximation version of the results of D. P. Gupta [ J. of Approx. Theory, 7 (1973), 226-238] A. N. S. Singroura [Proc. Japan Acad., 39 (4) (1963), 208-210] and G. S…
On estimates of deviation of conjugate functions from matrix operators of their Fourier series by some expressions with -differences of the entries
Wlodzimierz Lenski, Bogdan Szal
We extend the results of the authors from [Abstract and Applied Analysis, Volume 2016, Article ID 9712878] to the case conjugate Fourier series.
Estimates of convolution operators of functions from
Wlodzimierz Lenski, Bogdan Szal
We generalize and slight improve the result of I. I. Sharapudinov [Mat. Zametki, 1996, Volume 59, Issue 2, 291--302]. Some applications to the de la Vallée Poussin operator will al…
Pointwise strong approximation of almost periodic functions in S^1
Wlodzimierz Lenski, Bogdan Szal
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of S^1 almost periodic functions from matrix means of partial sums of their Fourier series.
On the degree of strong approximation of almost periodic functions in the Stepanov sense
Wlodzimierz Lenski, Bogdan Szal
Considering the class of almost periodic functions in the Stepanov sense we extend and generalize the results of the first author [4]. as well as the results of L. Leindler [3] and…
Pointwise strong approximation of almost periodic functions
Radosława Kranz, Włodzimierz Łenski, Bogdan Szal
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.
On some Leindler's theorem on application of the class NMCS
Włodzimierz Łenski, Bogdan Szal
We show the results in the class GM(5b) corresponding to the theorem of L. Leindler [A note on strong approximation of Fourier series, Analysis Mathematica, 29(2003), 195--199] on…
Strong approximation of almost periodic functions
Włodzimierz Łenski, Bogdan Szal
We consider summability methods generated by the class GM(2b). We generalize some related results of P. Pych-Taberska [Studia Math. XCVI (1990), 91-103] on strong approximation of…
Pointwise strong and very strong approximation by Fourier series of integrable functions
Włodzimierz Łenski
We will present an estimation of the and means as a approximation versions \ of \ the Totik type generalization$(\text{see \cite{11, 12}}…
Pointwise analog of the Stečkin approximation theorem
Włodzimierz Łenski
We show the pointwise version of the Stečkin theorem on approximation by de la Vallée-Poussin means. The result on norm approximation is also derived.