On Necessary and Sufficient Conditions for Absolute Matrix Summability

Abstract

This study gets a new general theorem related to necessary and sufficient conditions for $\varphi-{\mid D,\beta;\delta\mid}_{k}$ summability of the series $\sum a_n \lambda_n$ whenever the series $\sum a_n$ is summable $\varphi-{\mid C,\beta;\delta\mid}$, where $C=(c_{nv})$ and $D=(d_{nv})$ are two positive normal matrices, $k\geq 1$, $\delta\geq 0$ and $-\beta(\delta{k}+k-1)+k > 0$.