Necessary and Sufficient Conditions for Inclusion Relations for Absolute Summability

[摘要] We obtain a set of necessary and sufficient conditions for $| overline{N}, p_n|_k$ to imply $|overline{N}, q_n|_s$ for 1 < 𝑘 ≤ 𝑠 < ∞. Using this result we establish several inclusion theorems as well as conditions for the equivalence of $|overline{N}, p_n|_k$ and $|overline{N}, q_n|_s$.

[学科分类] 数学（综合）

[关键词] Absolute summability;weighted mean matrix;Cesáro matrix.