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.

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 Absolute weighted arithmetic mean summability factors of infinite series and trigonometric fourier series

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4963-4968 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Arithmetic Mean ◽  
Trigonometric Fourier Series ◽  
Summability Factors ◽  
Weighted Arithmetic ◽  
Quasi Power Increasing Sequence

In this paper, we generalized a known theorem dealing with absolute weighted arithmetic mean summability of infinite series by using a quasi-f-power increasing sequence instead of a quasi-?-power increasing sequence. And we applied it to the trigonometric Fourier series

scholarly journals Local properties of absolute matrix summability of factored fourier series

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4897-4903 ◽  
Author(s):  
Hikmet Özarslan ◽  
Şebnem Yıldız
Keyword(s):  
Fourier Series ◽  
Summability Factors ◽  
Matrix Summability ◽  
Absolute Matrix Summability ◽  
Summability Methods ◽  
Local Properties

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.

scholarly journals A general matrix application of convex sequences to Fourier series

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2443-2449
Author(s):  
Şebnem Yıldız
Keyword(s):  
Fourier Series ◽  
Local Property ◽  
Weighted Mean ◽  
General Matrix ◽  
Normal Matrices ◽  
Matrix Application ◽  
Convex Sequence ◽  
Weighted Mean Matrices ◽  
Local Properties ◽  
Appl Math

By using a convex sequence Bor [H. Bor, Local properties of factored Fourier series, Appl. Math. Comp. 212 (2009) 82-85] has obtained a result dealing with local property of factored Fourier series for weighted mean summability. The purpose of this paper is to extend this result to more general cases by taking normal matrices in place of weighted mean matrices.

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 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.

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