## Taiwanese Journal of Mathematics

### A CHARACTERIZATION OF ABSOLUTE SUMMABILITY FACTORS

#### Abstract

Let $A$ and $B$ be two summability methods. We shall use the notation $\lambda \in(A, B)$ to denote the set of all sequences $\lambda$ such that $\sum\nolimits a_{n}\lambda_{n}$ is summable $B$, whenever $\sum\nolimits a_{n}$ is summable $A$. In the present paper we characterize the sets $\lambda \in (|\overline{N}, p_{n}|, |T|_{k})$ and $\lambda \in (|\overline{N}, p_{n}|_{k}, |T|)$, where $T$ is a lower triangular matrix with positive entries and row sums $1$. As special cases we obtain summability factor theorems and inclusion theorems for pairs of weighted mean matrices.

#### Article information

Source
Taiwanese J. Math., Volume 8, Number 3 (2004), 453-465.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407665

Digital Object Identifier
doi:10.11650/twjm/1500407665

Mathematical Reviews number (MathSciNet)
MR2163318

Zentralblatt MATH identifier
1067.40004

#### Citation

Rhoades, B. E.; Savas, Ekrem. A CHARACTERIZATION OF ABSOLUTE SUMMABILITY FACTORS. Taiwanese J. Math. 8 (2004), no. 3, 453--465. doi:10.11650/twjm/1500407665. https://projecteuclid.org/euclid.twjm/1500407665

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