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On the Absolute Matrix Summability Factors of Fourier Series [PDF]

Mathematical Notes, 2018
WOS: 000427616800030In this paper, two known theorems on |NI", p (n) | (k) summability methods of Fourier series have been generalized for |A, p (n) | (k) summability factors of Fourier series by using different matrix transformations.
Ş. Yıldız, Yildiz, S.
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A note on absolute summability factors

Periodica Mathematica Hungarica, 2005
We obtain sufficient conditions for the series ]]> ]]> \sum a_{n}\lambda_{n}$ to be absolutely summable of order $k$ by a triangular matrix.
B. E. Rhoades, Ekrem Savas
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A summability factor theorem and applications

Applied Mathematics and Computation, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Savas, E, Rhoades, BE
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Absolute riesz summability factors

Periodica Mathematica Hungarica, 1989
The pioneer work of \textit{G. Sunouchi} [Kōdai Math. Seminar Reports 6, 59-62 (1954; Zbl 0057.300)] was generalized by Rath. The authors have extended Rath's result in the Indian J. Pure Appl. Math. 16, 1162-1180 (1985; Zbl 0586.40004)]. The present work is an improvement over author's previous results in the sense that here the result is obtained by ...
Sukla, Indulata, Mohanty, Peari Charan
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Some summability factor theorems for absolute summability

Analysis, 2002
The authors obtain a set of sufficient conditions on methods of summability and on sequences \(\left(e_n\right)\), so that \(\sigma a_n\) summable \(\left|\overline N,p_n\right|_k\) implies \(\sigma a_n e_n\) summable \(\left|T\right|_k\), with \(k\) greater than or equal to 1. As corollaries they obtain the results of \textit{W. T. Sulaiman} [Proc. Am.
Rhoades, B. E., Savaş, Ekrem
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Summability factors for generalized absolute summability. II

2001
Summary: A new theorem concerning the characterization of absolute summability factors has been proved. [For Part I and III see ibid. 31--39 (2001; Zbl 1078.40501) and 47--52 (2001; Zbl 1078.40502).]
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Absolute Summability Factors in a Sequence

Canadian Mathematical Bulletin, 1984
AbstractLet α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (εn) in order that the sequence (εnUn) will be absolutely summable by the Cesàro method Cβ for each sequence (Un) which is bounded or summable by the method CαAnother theorem is proven when Cα and Cβ are replaced by triangular methods A = (ank) and ...
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Absolute Summability Factors

Journal of the London Mathematical Society, 1970
Irwin, R. L., Peterson, G. E.
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On the Summability Factors of Fourier Series

Journal of the London Mathematical Society, 1941
Die Fourierreihe der mit \(2\pi\) periodischen, \(L\)-integrablen Funktion \(f(x)\) sei \[ f(x)\sim\tfrac12a_0+{\sum\limits_{n=1}^{\infty}} (a_n \cos nx+ b_n\sin nx)\equiv\tfrac12 c_0+{\sum\limits_{n=1}^{\infty}}c_n(x). \] Anknüpfend an ein Ergebnis von \textit{B. N. Prasad} [Proc. Lond. Math. Soc. (2) 35, 407--424 (1933; Zbl 0007.16003)] haben \textit{
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Absolute Cesàro summability factors

2002
The author intends to generalize a theorem concerning \(|C,1|_k\) summability factors to \(|C,\alpha, \beta, \delta|_k\) summability using \(\delta\)-quasi-monotone sequences. Unfortunately his Lemma 3 is not correct, consequently the proof of the theorem is not complete. The author will publish a correction soon (personal information).
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