scholarly journals Strong Riesz summability of Fourier series

2020 ◽  
Vol 39 (6) ◽  
pp. 1615-1626
Author(s):  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray ◽  
Umakanta Misra
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Sufficient Condition ◽  
Riesz Summability ◽  
Summability Of Fourier Series

The notion of strong summability was introduced by Fekete (Math. És Termesz Ertesitö, 34 (1916), 759-786). Dealing with Nörlund summability of Fourier series Mittal (J. Math. Anal. Appl. 314 (2006), 75-84) has established a result on strong summability. We have established a new result on sufficient condition for strong Riesz summability of Fourier series.

scholarly journals The strong summability of Fourier series

1935 ◽  
Vol 25 ◽  
pp. 162-189 ◽  
Author(s):  
G. Hardy ◽  
J. Littlewood
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Summability Of Fourier Series

On the Nørlund Summability of a Class of Fourier Series

1970 ◽  
Vol 22 (1) ◽  
pp. 86-91 ◽  
Author(s):  
Badri N. Sahney
Keyword(s):  
Fourier Series ◽  
Integrable Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Lebesgue Integrable Function ◽  
Summability Of Fourier Series ◽  
Lebesgue Set ◽  
Necessary And Sufficient

1. Our aim in this paper is to determine a necessary and sufficient condition for N∅rlund summability of Fourier series and to include a wider class of classical results. A Fourier series, of a Lebesgue-integrable function, is said to be summable at a point by N∅rlund method (N, pn), as defined by Hardy [1], if pn → Σpn → ∞, and the point is in a certain subset of the Lebesgue set. The following main results are known.

scholarly journals On absolute riesz summability of Fourier series

1975 ◽  
Vol 19 (1) ◽  
pp. 97-102
Author(s):  
G. D. Dikshit
Keyword(s):  
Fourier Series ◽  
General Theorem ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Summability Of Fourier Series ◽  
Image Position

AbstractLet and .In 1951 Mohanty proved the following theorem: .In this paper a general theorem on summability |R,l (w), 1 | of Σ An(x) has been given which improves upon Mohanty's result in different ways (see Corollaries 1, 2 and 3) and it is also shown that some of the results of this note are the best possible.

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