the object of this paper is to establish a summability factor theorem for summabilitya, , k  1 k  where a is the lower triangular matrix with non-negative entries satisfying certain conditions.

we obtain sufficient conditions for the series σanλn to be absolutely summable of order k by atriangular matrix.

In this paper we have proved two theorems concerning an inclusion between two absolute summability methods by using any absolute summability factor.

A triangle is a lower triangular matrix with all principal diagonal entriesbeing nonzero. Given an almost increasing sequence {Xn} and a sequence {λn} satisfying certain conditions, we obtain sufficient conditions for the series ∑ anλn to be absolutely summable of order k ≥ 1 by a triangle T . As a corollary we obtain the corresponding result when T is a weighted mean matrix. Theorem 1 of this ...

In the recent papers [1, 2], the author obtained necessary and sufficient conditions for a series ∑ an which is absolutely summable of order k by a weighted mean method, 1 < k ≤ s <∞, to be such that anλn is absolutely summable of order s by a triangular matrix method. In this paper, we obtain sufficient and (different) necessary conditions for a series ∑ an which is absolutely summable |A|k to...

Inclusion of absolute summability domains of matrices Factorable matrices Summability method of Cesàro a b s t r a c t In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely conve...