scholarly journals An absolute matrix summability of infinite series and Fourier series

2019 ◽  
Vol 38 (7) ◽  
pp. 49-58
Author(s):  
Sebnem Yildiz
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Vital Role ◽  
The Other ◽  
Weighted Mean ◽  
Matrix Summability ◽  
Absolute Matrix Summability

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.

scholarly journals A new theorem on absolute matrix summability of fourier series

2017 ◽  
Vol 102 (116) ◽  
pp. 107-113 ◽  
Author(s):  
Şebnem Yildiz
Keyword(s):  
Fourier Series ◽  
Summability Factors ◽  
Weighted Mean ◽  
Matrix Summability ◽  
Absolute Matrix Summability ◽  
Summability Of Fourier Series ◽  
Weaker Conditions

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.

scholarly journals An application of quasi-monotone sequences to absolute matrix summability

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3709-3715 ◽  
Author(s):  
Şebnem Yıldız
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Method ◽  
Summability Factors ◽  
Matrix Summability ◽  
Absolute Matrix Summability ◽  
Monotone Sequences

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.

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

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4343-4351
Author(s):  
Şebnem Yıldız
Keyword(s):  
Fourier Series ◽  
General Theorem ◽  
Arithmetic Mean ◽  
Summability Factors ◽  
Weighted Mean ◽  
Normal Matrices ◽  
Matrix Summability ◽  
Absolute Matrix Summability ◽  
Weighted Arithmetic ◽  
Weighted Mean Matrices

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.

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