Results 221 to 230 of about 4,014 (264)

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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Inequalities for summability factors

1992
We consider two inequalities which are relevant for Cesaro summability factors. Combined use of these inequalities (in the realm of B K -spaces) leads to a rather short and lucid verification of Bosanquet’s theorem.
W. Beekmann, K. Zeller
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Absolute Summability Factors

Journal of the London Mathematical Society, 1970
Irwin, R. L., Peterson, G. E.
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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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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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STRONG CESÀRO SUMMABILITY FACTORS

The Quarterly Journal of Mathematics, 1970
Kuttner, Brian, Maddox, I. J.
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General Summability Factor Theorems and Applications

Sarajevo Journal of Mathematics
We obtain sufficient and (different) necessary conditions for the series $\sum a_{n}$, which is absolutely summable of order $k$ by a triangular matrix method $A$, to be such that $\sum a_{n}\lambda_n$ is absolutely summable of order $k$ by a triangular matrix $B$. As corollaries we obtain a number of inclusion theorems.
Rhoades, B. E., Savaş, Ekrem
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Summability factors for generalized absolute summability. II

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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Summability Factors^†

Proceedings of the London Mathematical Society, 1969
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Summability Factors for Generalized Absolute Summability. I

Proceedings of the London Mathematical Society, 1960
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