Real Analysis Exchange

A summability factor theorem for generalized absolute summability.

B. E. Rhoades and Ekrem Savaş

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Abstract

In this paper, we establish a summability factor theorem for summability $|A,\delta|_k$ as defined in (\ref{eq2}) where $A$ is a lower triangular matrix with non-negative entries satisfying certain conditions. Our paper is an extension of a result of Bor and Seyhan (1999) using definition (1) below.

Article information

Source
Real Anal. Exchange, Volume 31, Number 2 (2005), 355-363.

Dates
First available in Project Euclid: 10 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184104029

Mathematical Reviews number (MathSciNet)
MR2265778

Zentralblatt MATH identifier
1116.40004

Subjects
Primary: 40F05: Absolute and strong summability (should also be assigned at least one other classification number in Section 40) 40D25: Inclusion and equivalence theorems

Keywords
absolute summability almost increasing summability factors

Citation

Rhoades, B. E.; Savaş, Ekrem. A summability factor theorem for generalized absolute summability. Real Anal. Exchange 31 (2005), no. 2, 355--363. https://projecteuclid.org/euclid.rae/1184104029


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References

  • H. Bor, H. Seyhan, On Almost Increasing Sequence and its Applications, Indian J. Pure appl. Math., 30 (1999), 1041–1046.
  • T. M. Fleet, On an Extension of Absolute Summability and Some Theorems of Littlewood and Paley, Proc. London Math. Soc., 3, 7 (1957), 113–141.
  • B. E. Rhoades, Inclusion Theorems for Absolute Matrix Summability Methods, J. Math. Anal. Appl., 238 (1999), 82–90.
  • E. Savaş, On generalized absolute summability factor theorem, Nonlinear Analy., preprint.