Characterization of general summability factors and applications

By (A,B)(A,B), we denote the set of all sequences ϵϵ such that ΣϵnxnΣϵnxn is summable by BB whenever ΣxnΣxn is summable by AA, where AA and BB 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)ϵ∈(A,B), and also deduced various known and some new results as special cases.