A note on absolute summability factors

In this paper, by using an almost increasing and $\delta$-quasi-monotone sequence, a general theorem on $\varphi -{\mid C,\alpha \mid }_k$ summability factors, which generalizes a result of Bor \cite{3} on ${\varphi -\mid C,1\mid }_k$ summability factors, has been proved under weaker and more general conditions.