A new factor theorem on absolute matrix summability method

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

A new result on the quasi power increasing sequences

This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence.

An absolute matrix summability of infinite series and Fourier series

The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power sequences.

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.

On the generalizations of some factors theorems for infinite series and fourier series

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.