Approximation of integrable functions by general linear matrix operators of their Fourier series

• Autorzy: Mishra Vishnu Narayan , Łenski Włodzimierz , Szal Bogdan

Identyfikatory

DOI

10.1515/dema-2022-0009

• Języki publikacji: EN

Abstrakty

EN

The pointwise estimates of the deviation Tn,Af(⋅)−f(⋅) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f , with application of the rth differences of the entries of A , are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.

Słowa kluczowe

EN

rate of approximation; summability of Fourier series

PL

aproksymacja; szeregi Fouriera

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 136--152
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Mishra Vishnu Narayan

• Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

autor

Łenski Włodzimierz

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-516 Zielona Góra, ul. Szafrana 4a, Poland

autor

Szal Bogdan

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-516 Zielona Góra, ul. Szafrana 4a, Poland

Bibliografia

• [1] P. Chandra, Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275 (2002), 13–26.
• [2] L. Leindler, Trigonometric approximation in Lp-norm, J. Math. Anal. Appl. 302 (2005), 129–136.
• [3] W. Łenski, On the rate of pointwise strong C α,( ) summability of Fourier series, Colloquia Math. Soc. János Bolyai 58 (1990), 453–486, Approx. Theory, Kecskemét (Hungary).
• [4] M. L. Mittal, B. E. Rhoades, V. N. Mishra, and U. Singh, Using infinite matrices to approximate functions of class Lip α p,( ) using trigonometric polynomials, J. Math. Anal. Appl. 326 (2007), 667–676.
• [5] R. Taberski, On the convergence of singular integrals (in Polish), Zeszyty Nauk. Uniw. Mickiewicza 25 (1960), 33–51.
• [6] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, 2002.
• [7] W. Łenski, On the rate of pointwise summability of Fourier series, Applied Math. E-Notes 1 (2001), 143–148.
• [8] B. Szal, A new class of numerical sequences and its applications to uniform convergence of sine series, Math. Nachr. 284 (2011), no. 14–15, 1985–2002.
• [9] B, Szal, On L-convergence of trigonometric series, J. Math. Anal. Appl. 373 (2011), 449–463.
• [10] W. Łenski and B. Szal, Approximation of integrable functions by general linear operators of their Fourier series, Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 6, 1119–1134.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).