In this paper, we have generalized a known theorem dealing with $\varphi-{\mid{C},\alpha,\mid}_k$ summability factors of infinite series to the $\varphi-{\mid{C},\alpha,\beta\mid}_k$ summability method under weaker conditions. Also, some new and known results are obtained.
UDC 517.54
The aim of the paper is a generalization, under weaker conditions, of the main theorem on quasi-
σ
-power increasing sequences applied to
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A
,
θ
n
|
k
summability factors of infinite series and Fourier series. We obtain some new and known results related to basic summability methods.
Abstract
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.
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.
On absolute matrix summability factors of infinite series and Fourier series