A new factor theorem for generalized absolute Riesz summability

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.

On absolute Riesz summability factors of infinite series and their application to Fourier series

In this paper, some known results on the absolute Riesz summability factors of infinite series and trigonometric Fourier series have been generalized for the {\lvert\bar{N},p_{n};\theta_{n}\rvert_{k}} summability method. Some new and known results are also obtained.

On a new application of quasi power increasing sequences

In the present paper, absolute matrix summability of infinite series has been studied. A new theorem concerned with absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, has been proved under weaker conditions by using quasi $\beta$-power increasing sequences. Also, a known result dealing with absolute Riesz summability has been given.