An Estimate of the Rate of Convergence of the Fourier Series in the Generalized Hölder Metric by Delayed Arithmetic Mean

L. Nayak, G. Das, B. K. Ray

Type: Article

Publication Date: 2014-05-07

Citations: 7

DOI: https://doi.org/10.1155/2014/171675

Abstract

We study the rate of convergence problem of the Fourier series by Delayed Arithmetic Mean in the generalized Hölder metric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math> space which was earlier introduced by Das, Nath, and Ray and obtain a sharper estimate of Jackson's order.

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International Journal of Analysis - View - PDF

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Works Cited by This (5)

Action	Title	Year	Authors
+	A relaxed estimate of the degree of approximation by Fourier series in generalized Hölder metric	2009	Л. Леиндлер
+	On the strong approximation of Fourier series	1980	Вилмос Тотик
+	Approximation of continuous functions by T-means of Fourier series	1990	S. M. Mazhar Вилмос Тотик
+	Degree of approximation of functions by their fourier series in the generalized Hölder metric	1996	G. Das Tulika Ghosh B. K. Ray
+	Zur Konvergenz der Fourierreihen hölderstetiger Funktionen	1975	Siegfried Prößdorf