On a summability factor theorem

A New Factor Theorem on Absolute Riesz Summability

A New Factor Theorem for Generalized Cesàro Summability

In [6], we proved a theorem dealing with an application of quasi-f-power increasing sequences. In this paper, we prove that theorem under less and weaker conditions. This theorem also includes several new results.

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 ...

A Summability Factor Theorem for Quasi-Power-Increasing Sequences

Correspondence should be addressed to E. Savaş, [email protected] Received 23 June 2010; Revised 3 September 2010; Accepted 15 September 2010 Academic Editor: J. Szabados Copyright q 2010 E. Savaş. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work ...