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.
We generalize a main theorem dealing with absolute weighted mean summability
of Fourier series to the |A,pn|k summability factors of Fourier series
under weaker conditions. Also some new and known results are obtained.
In this paper, we introduce two new general theorems on ??A,pn?k summability
factors of infinite and Fourier series. By using these theorems, we obtain
some new results regarding other important summability methods and
investigate conversions between them.
Recently, Bor [5] has obtained two main theorems dealing with |?N,pn|k
summability factors of infinite series and Fourier series. In the present
paper, we have generalized these theorems for |A,?n|k summability method by
using quasi-monotone sequences.
Abstract
In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods
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
|
A
,
θ
n
|
k
summability factors of infinite series and Fourier series. We obtain some new and known results related to basic summability methods.
Quite recently, Bor [Quaest. Math. (doi.org/10.2989/16073606.2019.1578836, in
press)] has proved a new result on weighted arithmetic mean summability
factors of non decreasing sequences and application on Fourier series. In
this paper, we establish a general theorem dealing with absolute matrix
summability by using an almost increasing sequence and normal matrices in
place of a positive non-decreasing sequence and weighted mean matrices,
respectively. So, we extend his result to more general cases.
On a new application of quasi power increasing sequences
