On the approximation of functions from L^p by some special matrix means of Fourier series

• Autorzy: Kranz R. , Rzepka A.

Identyfikatory

DOI

0.1515/fascmath-2015-0016

• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

degree of approximation; Fourier series; matrix means

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 55
• Strony: 81--90
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Kranz R.

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

autor

Rzepka A.

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

Bibliografia

• [1] Lal S., Approximation of functions belonging to the generalized Lipschitz Class by C1 Np summability method of Fourier series, Applied Mathematics and Computation, 209(2009), 346-350.
• [2] Leindler L., Integrability conditions pertaining to Orlicz space, J. Inequal. Pure and Appl. Math., 8(2)(2007), Art. 38, 6 pp.
• [3] Łenski W., Szal B., Approximation of functions from L^p (ω)_β by general linear operators of their Fourier series, Banach Center Publ., 95(2011), 339-351.
• [4] Zygmund A., Trigonometric series, Cambridge, 2002.