Abstract
The aim of this paper is to consider an absolute summability method and generalize a theorem concerning $\left|\bar{N},p_{n}\right|_{k}$ summability of infinite series to ${\varphi-\mid{\bar{N},p_n;\delta}\mid}_k$ summability of infinite series by using almost increasing sequence. Furthermore, it is explained that a well known result dealing with $\left|\bar{N},p_{n}\right|_{k}$ summability is obtained when this generalization is restricted under special conditions.
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