• Necessary and sufficient conditions for inclusion relations for absolute summability

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/113/03/0243-0250

• # Keywords

Absolute summability; weighted mean matrix; Cesáro matrix

• # Abstract

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

• # Author Affiliations

1. Department of Mathematics, Indiana University, Bloomington, IN - 47405-7106, USA
2. Department of Mathematics, Yüzüncü Yil University, Van, Turkey

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019