On inclusion relations for absolute summability (Q1854135)

Summary: We obtain necessary and (different) sufficient conditions for a series summable \(|\overline N,p_{n}|_k\), \(1<k\leq s<\infty\), to imply that the series is summable \(|T|_{s}\), where \((\overline N,p_{n})\) is a weighted mean matrix and \(T\) is a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems.