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

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 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 ...

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 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 Recent Note on Quasi-Power Increasing Sequence for Generalized Absolute Summability

Quite recently, Savaş 1 obtained sufficient conditions for ∑ anλn to be summable |A, δ|k, k ≥ 1, 0 ≤ δ < 1/k. The purpose of this paper is to obtain the corresponding result for quasif-increasing sequence. Our result includes and moderates the conditions of his theorem with the special case μ 0. A sequence {λn} is said to be of bounded variation bv if ∑ n |Δλn| < ∞. Let bv0 bv ∩ c0, where c0 de...

A New Factor Theorem on Absolute Riesz Summability