On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$

Abstract

Recently, for single series, the necessary and sufficient conditions for $\left\vert C,0\right\vert\Rightarrow \left\vert A_{f}\right\vert_{k}$ and vise versa, and $\left\vert A_{f}\right\vert \Rightarrow \left\vert C,0\right\vert_{k}$ and vise versa have been established, where $1 < k < \infty $ and $A$ is a factorable matrix. The present study extends these results to double summability, and also provides some new results.