Some new factor theorem for absolute summability

A New Factor Theorem on Absolute Riesz Summability

a generalized summability factor theorem for absolute summability and quasi   power increasing sequences

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.

a summability factor theorem for absolute summability involving quasi power increasing sequences

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

A summability factor theorem involving an almost increasing sequence for generalized absolute summability

In this paper we prove a general theorem on |A; δ|k -summability factors of infinite series under suitable conditions by using an almost increasing sequence, where A is a lower triangular matrix with non-negative entries. Also, we deduce a similar result for the weighted mean method. c © 2007 Elsevier Ltd. All rights reserved.

A summability factor theorem for absolute summability involving almost increasing sequences

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 ...