On pointwise approximation of functions by some matrix means of conjugate Fourier series

• Autorzy: Łenski W. , Szal B.

Identyfikatory

DOI

0.1515/fascmath-2015-0017

• Języki publikacji: EN

Abstrakty

EN

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 Norlund or the Riesz method with the Euler one are also formulated.

Słowa kluczowe

EN

conjugate function; Fourier series; degree of approximation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 55
• Strony: 91--108
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Łenski W.

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

autor

Szal B.

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

Bibliografia

• [1] Lal S., Nigam H.K., Degree of approximation of conjugate of a function belonging to Lip (ξ (t) ,p) class by matrix summability means of conjugate Fourier series, Int. J. Math. Math. Sci., 27(9)(2001), 555-563.
• [2] Lal S., On the degree of approximation of conjugate of a function belonging to weighted W (L^p, ξ (t)) class by matrix summability means of conjugate series of a Fourier series, Tamkang J. Math., 31(4)(2000), 279-288.
• [3] Leindler L., On the degree of approximation of continuous functions, Acta Math. Hungar, 104(1-2)(2004), 105-113.
• [4] Leindler L., Integrability conditions pertaining to Orlicz space, J. Inequal. Pure and Appl. Math., 8(2)(2007), Art. 38, 6 pp.
• [5] Łenski W., Szal B., Approximation of functions belonging to the class L^p (ω)_β by linear operators, Acta Comment. Univ. Tartu. Math., 13(2009), 11-24.
• [6] Łenski W., Szal B., Approximation of functions from L^p (ῶ)_βby linear operators of conjugate Fourier series, Banach Center Publ., 92(2011), 237-247.
• [7] 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., 12(9)(1981), 1120-1123.
• [8] 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., 13(5)(1982), 560-563.
• [9] 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.
• [10] Szal B., A note on the uniform convergence and boundedness a generalized class of sine series, Commentat. Math., 48(1)(2008), 85-94.
• [11] Zygmund A., Trigonometric series, Cambridge, 2002.