Characterization of general summability factors and applications

AbstractBy (A,B), we denote the set of all sequences ϵ such that Σϵnxn is summable by B whenever Σxn is summable by A, where A and B are some summability methods. In this paper, we established a simple set of necessary and sufficient conditions for summability factor of type ϵ∈(A,B), and also deduced various known and some new results as special cases