Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 10892, 10 pages
doi:10.1155/2007/10892
Research Article
On General Summability Factor Theorems
Department of Mathematics, Faculty of Science and Arts, Istanbul Ticaret University, Uskudar, Istanbul 34672, Turkey
Received 17 August 2006; Revised 6 December 2006; Accepted 2 January 2007
Academic Editor: Ram Mohapatra
Copyright © 2007 Ekrem 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 is properly cited.
Abstract
The goal of this paper is to obtain sufficient and (different)
necessary conditions for a series ∑an, which is absolutely summable of order k by a triangular matrix method A, 1<k≤s<∞, to be such that ∑anλn is absolutely summable of order s by a triangular matrix method B. As corollaries, we obtain two inclusion theorems.