scholarly journals Pointwise approximation of functions by matrix operators of their Fourier series with r-differences of the entries

2020 ◽  
Vol 60 (4) ◽  
pp. 494-512
Author(s):  
Włodzimierz Łenski ◽  
Bogdan Szal
Keyword(s):  
Fourier Series ◽  
Pointwise Approximation ◽  
Approximation Of Functions ◽  
Matrix Operators

scholarly journals On the Approximation of Functions From Lp by Some Special Matrix Means of Fourier Series

2015 ◽  
Vol 55 (1) ◽  
pp. 81-90
Author(s):  
Radosława Kranz ◽  
Aleksandra Rzepka
Keyword(s):  
Fourier Series ◽  
Pointwise Approximation ◽  
Approximation Of Functions ◽  
Summability Methods ◽  
Matrix Means ◽  
Special Cases ◽  
Special Matrix ◽  
Norm Approximation ◽  
Appl Math

Abstract The results corresponding to some theorems of S. Lal [Appl. Math. and Comput. 209 (2009), 346-350] and the results of W. Łenski 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.

scholarly journals On Pointwise Approximation of Functions by Some Matrix Means of Conjugate Fourier Series

2015 ◽  
Vol 55 (1) ◽  
pp. 91-108
Author(s):  
W. Lenski ◽  
B. Szal
Keyword(s):  
Fourier Series ◽  
Pointwise Approximation ◽  
Approximation Of Functions ◽  
Conjugate Fourier Series ◽  
Riesz Method ◽  
Matrix Means ◽  
Special Cases ◽  
Norm Approximation

Abstract The results corresponding to some theorems of S. Lal [Tamkang J. Math., 31(4)(2000), 279-288] and the results of the authors [Banach Center Publ. 92(2011), 237-247] are shown. The same degrees of pointwise approximation as in mentioned papers by significantly weaker assumptions on considered functions are obtained. From presented pointwise results the estimation on norm approximation with essentialy better degrees are derived. Some special cases as corollaries for iteration of the Nörlund or the Riesz method with the Euler one are also formulated.

scholarly journals Pointwise approximation of 2 π/r-periodic functions by matrix operators of their Fourier series with r-differences of the entries

2018 ◽  
Vol 51 (1) ◽  
pp. 309-322
Author(s):  
Włodzimierz Łenski ◽  
Bogdan Szal
Keyword(s):  
Fourier Series ◽  
Periodic Functions ◽  
Pointwise Approximation ◽  
Matrix Operators

Abstract 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 2 π/r-periodic functions. Moreover, as a measure of approximation r-differences of the entries are used.

scholarly journals Pointwise Approximation of Functions from by Linear Operators of Their Fourier Series

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Włodzimierz Łenski ◽  
Bogdan Szal
Keyword(s):  
Fourier Series ◽  
Linear Operators ◽  
Pointwise Approximation ◽  
Approximation Of Functions ◽  
Lipschitz Classes ◽  
Matrix Summability

We show the results, corresponding to theorem of Lal (2009), on the rate of pointwise approximation of functions from the pointwise integral Lipschitz classes by matrix summability means of their Fourier series as well as the theorems on norm approximations.

scholarly journals Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series with the use of some parameters

2020 ◽  
Vol 51 (2) ◽  
pp. 145-159
Author(s):  
Bogdan Szal ◽  
Wlodzimierz Lenski
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Conjugate Function ◽  
Conjugate Functions ◽  
Pointwise Approximation ◽  
Matrix Operators

We extend and generalize the results of Xh. Z. Krasniqi [Acta Comment. Univ.Tartu. Math. 17 (2013), 89-101] and the authors [Acta Comment. Univ. Tartu.Math. 13 (2009), 11-24], [Proc. Estonian Acad. Sci. 2018, 67, 1, 50--60] aswell the jont paper with M. Kubiak [Journal of Inequalities and Applications(2018) 2018:92]. We consider the modified conjugate function  $\widetilde{f}%_{r}$ for $2\pi /\rho $--periodic function $f$ . Moreover, the measure ofapproximations depends on \textbf{\ }$\mathbf{\rho }$\textbf{ - }differencesof the entries of matrices defined the method of summability.

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