Factor relations between some summability methods

Abstract

In the present paper, using the result of Bennett [1] on characterization of factorable matrices, we give necessary and sufficient conditions in order that Σλ_{n}x_{n} is summable |R,p_{n}|_{s} whenever Σμ_{n}x_{n} is summable |C,0|_{k}, and Σλ_{n}x_{n} is summable |C,0|_{s} whenever Σμ_{n}x_{n} is summable |R,p_{n}|_{r},. where 1