Summability Factor Theorem Research Articles

On General Summability Factor Theorems

The goal of this paper is to obtain sufficient and (different) necessary conditions for a series , which is absolutely summable of order by a triangular matrix method , , to be such that is absolutely summable of order by a triangular matrix method . As corollaries, we obtain two inclusion theorems.

On the generalized absolute summability factor theorem

In this paper, we establish a summability factor theorem for summability | A | k where A is a lower triangular matrix with non-negative entries satisfying certain conditions.

A Summability Factor Theorem for Generalized Absolute Summability

In this paper, we establish a summability factor theorem for summability |A, |k as defined in (1) where A is a lower triangular matrix with non-negative entries satisfying certain conditions. Our paper is an extension of the main result of [1] using definition (1) below. Recently, Bor and Seyhan [1] proved a theorem on | ¯ N,p, |k summability factor under weaker conditions by using an almost increasing sequence. Unfortunately they used an incorrect definition, (for detail, see, [3]). In this paper, we generalize their result by using the correct definition and a lower triangular matrix with non-negative entries satisfying certain conditions. Let A be a lower triangular matrix, {sn} a sequence. Then

A Summability Factor Theorem for Infinite Series

We obtain sufficient conditions for the series $\sum\nolimits a_{n}\lambda_n$ to be absolutely summable of order $k$ by a triangular matrix.

A CHARACTERIZATION OF ABSOLUTE SUMMABILITY FACTORS

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.

A summability factor theorem for absolute summability involving almost increasing sequences

We obtain sufficient conditions for the series ∑anλn to be absolutely summable of order k by a triangular matrix.

A summability factor theorem and applications

We obtain sufficient conditions for the series ∑ a n , which is absolutely summable of order k by a weighted mean method, to be such that ∑ ϵ n a n is absolutely summable of order k by a triangular matrix. As corollaries we obtain a number of inclusion theorems.

Local property of absolute weighted mean summability of Fourier series

We obtain a theorem on a local property of | N,p n| k summability of factored Fourier series and a summability factor theorem for Fourier series.

Some summability factor theorems for absolute summability

Some summability factor theorems for absolute summability

A strong-Riesz mean-value theorem with applications to summability factor theorems.

Article A strong-Riesz mean-value theorem with applications to summability factor theorems. was published on January 1, 1978 in the journal Journal für die reine und angewandte Mathematik (volume 1978, issue 298).

On a Summability Factor Theorem for Riesz Means

On a Summability Factor Theorem for Riesz Means

Some Summability Factor Theorems for Infinite Integrals

Some Summability Factor Theorems for Infinite Integrals

A Summability Factor Theorem

A Summability Factor Theorem