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.
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.
A new theorem on absolute matrix summability of fourier series
