Necessary and sufficient conditions for inclusion relations for absolute summability

Abstract

We obtain a set of necessary and sufficient conditions for $|\bar{N},p_n{|}_k$ to imply $|\bar{N},q_n{|}_s$ for $1<k\le s<\infty$. Using this result we establish several inclusion theorems as well as conditions for the equivalence of $|\bar{N},p_n{|}_k$ and $|\bar{N},q_n{|}_s$.

8 pages, no figures