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 a new application of quasi power increasing sequences

2019 ◽  
Vol 11 (1) ◽  
pp. 152-157
Author(s):  
H.S. Özarslan
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
Matrix Summability ◽  
Absolute Matrix Summability ◽  
Riesz Summability ◽  
Beta Power ◽  
Absolute Riesz Summability ◽  
Power Increasing Sequences ◽  
Weaker Conditions ◽  
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.

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 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 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.

A new note on generalized absolute Cesàro summability factors

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3093-3096
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Method ◽  
Summability Factors ◽  
Cesàro Summability ◽  
Monotone Sequences ◽  
Cesaro Summability ◽  
Power Increasing Sequences ◽  
Increasing Sequences ◽  
General Summability

Quite recently, in [10], we have proved a theorem dealing with the generalized absolute Ces?ro summability factors of infinite series by using quasi monotone sequences and quasi power increasing sequences. In this paper, we generalize this theorem for the more general summability method. This new theorem also includes some new and known results.

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