Degrees of the approximations by some special matrix means of conjugate Fourier series

• Autorzy: Kranz Radosława , Rzepka Aleksandra , Sylwestrzak-Maślanka Ewa

Identyfikatory

DOI

10.1515/dema-2019-0014

• Języki publikacji: EN

Abstrakty

EN

In this paper we will present the pointwise and normwise estimations of the deviations considered by W. Łenski, B. Szal, [Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24] and S. Saini, U. Singh, [Boll. Unione Mat. Ital., 2016, 9, 495-504] under general assumptions on the class considered sequences defining the method of the summability. We show that the obtained estimations are the best possible for some subclasses of Lp by constructing the suitable type of functions.

Słowa kluczowe

EN

degree of approximation; Fourier series; matrix means

PL

aproksymacja; przybliżenie; szereg Fouriera; macierz

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 116--129
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Kranz Radosława

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

autor

Rzepka Aleksandra

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

autor

Sylwestrzak-Maślanka Ewa

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

Bibliografia

• [1] Zygmund A., Trigonometric series, Cambridge, 2002
• [2] Leindler L., On the degree of approximation of continuous functions, Acta Math. Hungar., 2004, 104 (1-2), 105-113
• [3] Szal B., A note on the uniform convergence and boundedness a generalized class of sine series, Commentat. Math., 2008,48(1), 85-94
• [4] Qureshi K., On the degree of approximation of functions belonging to the Lipschitz class by means of a conjugate series,Indian J. Pure Appl. Math., 1981, 12(9), 1120-1123
• [5] Lal S., Nigam H. K., Degree of approximation of conjugate of a function belonging to Lip (ξ(t) , p) class by matrix summabilitymeans of conjugate Fourier series, Int. J. Math. Math. Sci., 2001, 27(9), 555-563
• [6] Dhakal B. P., Approximation of the conjugate of function belonging to Lipα class by (E, 1) (C, 1) means of the conjugateseries of it’s Fourier series, Int. J. Innov. Res. Sci. Eng. Technol., 2013, 2(3), 836-840
• [7] Lal S., Singh G. K., Degree of approximation of conjugate of Lipα class function by K-summability means of conjugate seriesof a Fourier series, Tamkang J. Math., 2003, 34(4), 387-394
• [8] Mishra V. N., Khan H. H., Khatri K., Degree of approximation of conjugate of signals (functions) by lower triangular matrixoperator, App. Math., 2011, 2, 1448-1452
• [9] Mishra L. N., Mishra V. N., Sonavane V., Trigonometric approximation of functions belonging to Lipschitz class by matrix (C1·Np) operator of conjugate series of Fourier series, Adv. Difference Equ., 2013, 2013:127, 1-10
• [10] Nigam H. K., Sharma A., On approximation of conjugate of functions belonging to different classes by product means, Int.J. Pure Appl. Math., 2012, 76(2), 303-316
• [11] Rhoades B. E., The degree of approximation of functions, and their conjugates, belonging to several general Lipschitzclasses by Hausdorff matrix means of the Fourier series and conjugate series of a Fourier series, Tamkang J. Math., 2014,45(4), 389-395
• [12] Sonker S., Singh U., Degree of approximation of the conjugate of signals (functions) belonging to Lip(α, r)-class by (C, 1) (E, q) means of conjugate trigonometric Fourier series, J. Inequal. Appl , 2012, 2012:278, 1-7
• [13] Qureshi K., On the degree of approximation of functions belonging to the class Lip (α, p) by means of a conjugate series, Indian J. Pure Appl. Math., 1982, 13(5), 560-563
• [14] Łenski W., Szal B., Approximation of functions belonging to the class Lp (ω)β by linear operators, Acta Comment. Univ. Tartu.Math., 2009, 13, 11-24
• [15] Sain S., Singh U., Degree of approximation of function belonging to Lip(ω(t), p)-class by linear operators based on Fourierseries, Boll. Unione Mat. Ital., 2016, 9, 495-504
• [16] Łenski W., Szal B., Approximation of functions from Lp(̃ω)β by linear operators of conjugate Fourier series, Banach Center Publications, 2011, 92, 237-247
• [17] Totik V., On the strong approximation by the means of Fourier series I, Anal. Math., 1980, 6, 57-85

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).