scholarly journals An estimate of the rate of convergence of Fourier series in the generalized Hölder metric by Deferred Cesàro Mean

2014 ◽  
Vol 420 (1) ◽  
pp. 563-575 ◽  
Author(s):  
L. Nayak ◽  
G. Das ◽  
B.K. Ray
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Cesàro Mean ◽  
Hölder Metric ◽  
Cesaro Mean ◽  
Generalized Hölder Metric

On approximation of the rate of convergence of Fourier series in the generalized Hölder metric by Deferred Nörlund mean

2019 ◽  
Vol 30 (7-8) ◽  
pp. 1119-1131 ◽  
Author(s):  
T. Pradhan ◽  
B. B. Jena ◽  
S. K. Paikray ◽  
H. Dutta ◽  
U. K. Misra
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Hölder Metric ◽  
Generalized Hölder Metric

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

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
L. Nayak ◽  
G. Das ◽  
B. K. Ray
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Arithmetic Mean ◽  
Convergence Problem ◽  
Hölder Metric ◽  
Generalized Hölder Metric

We study the rate of convergence problem of the Fourier series by Delayed Arithmetic Mean in the generalized Hölder metric (Hp(w)) space which was earlier introduced by Das, Nath, and Ray and obtain a sharper estimate of Jackson's order.

On the Cesàro summability of Fourier series and Allied series

1930 ◽  
Vol 26 (2) ◽  
pp. 173-203 ◽  
Author(s):  
R. E. A. C. Paley
Keyword(s):  
Fourier Series ◽  
Cesàro Summability ◽  
Cesàro Mean ◽  
Cesaro Summability ◽  
Cesaro Mean ◽  
Summability Of Fourier Series ◽  
Image Position

For r>-1, let denoteIfwe say that the series a0 + a1 + a2 +…+an+… is summable by Cesàro mean of order r, or more shortly summable (C, r) to sum s. If r >−1, andwe say that the series is summable by Rieszian mean of order r to the sum s. It has been shown that these two methods of summation are equivalent. Throughout this paper I shall deal with the Rieszian mean, but I shall retain the symbol (C, r). It is known† that if a series is summable (C, r), it is also summable (C, r′) to the same sum for all numbers r′ greater than r.

Cesàro Means of Trigonometric Fourier Series

2002 ◽  
Vol 9 (1) ◽  
pp. 53-56
Author(s):  
U. Goginava
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Trigonometric Fourier Series ◽  
Cesàro Means ◽  
Cesàro Mean ◽  
Cesaro Means ◽  
Cesáro Means ◽  
Cesaro Mean

Abstract L. Zhizhiashvili proved that if for some 𝑝, 1 ≤ 𝑝 ≤ ∞, and α ∈ (0, 1), then the 𝐿𝑝-deviation of 𝑓 from its Cesàro mean is 𝑂(𝑛 α 𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1.

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