On General Summability Factor Theorems

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.