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STUDIA MATHEMATICA - Ediţia nr.3 din 2018

Articol:

A NOTE ON THE DEGREE OF APPROXIMATION OF FUNCTIONS BELONGING TO CERTAIN LIPSCHITZ CLASS BY ALMOST RIESZ MEANS.

Autori: UADAY SINGH, ARTI RATHORE.

Rezumat:

The problem of obtaining degree of approximation for the 2π−periodic functions in the weighted Lipschitz class W(L^p,ξ(t)) (p ≥ 1) by Riesz means of the Fourier series have been studied by various investigators under L^p−norm. Recently, Deepmala and Piscoran [Approximation of signals(functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series, J. Inequal. Appl., (2016), 2016:163. DOI 10.1186/s13660-016-1101-5] obtained a result on degree of approximation for weighted Lipschitz class by Riesz means. In this note, we extend this study to the weighted L^p−norm which in turn improves some of the previous results. We also derive some corollaries from our result.

Mathematics Subject Classiﬁcation (2010): 42A10, 42A24, 41A25. Keywords: Fourier series, degree of approximation, weighted L^p−norm, generalized Minkowski inequality, almost Riesz means.

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	STUDIA MATHEMATICA - Ediţia nr.3 din 2018

	Articol:	A NOTE ON THE DEGREE OF APPROXIMATION OF FUNCTIONS BELONGING TO CERTAIN LIPSCHITZ CLASS BY ALMOST RIESZ MEANS. Autori: UADAY SINGH, ARTI RATHORE.


	Rezumat: The problem of obtaining degree of approximation for the 2π−periodic functions in the weighted Lipschitz class W(L^p,ξ(t)) (p ≥ 1) by Riesz means of the Fourier series have been studied by various investigators under L^p−norm. Recently, Deepmala and Piscoran [Approximation of signals(functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series, J. Inequal. Appl., (2016), 2016:163. DOI 10.1186/s13660-016-1101-5] obtained a result on degree of approximation for weighted Lipschitz class by Riesz means. In this note, we extend this study to the weighted L^p−norm which in turn improves some of the previous results. We also derive some corollaries from our result. Mathematics Subject Classiﬁcation (2010): 42A10, 42A24, 41A25. Keywords: Fourier series, degree of approximation, weighted L^p−norm, generalized Minkowski inequality, almost Riesz means.




			Revenire la pagina precedentă