On Inclusion Relations for Absolute Summability

Abstract

We obtain necessary and (different) sufficient conditions for a series summable | N−, pn|k, 1<k≤s<∞, to imply that the series is summable |T|s, where (N−, pn) is a weighted mean matrix and T is a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems. © 2002 Hindawi Publishing Corporation. All rights reserved.