scholarly journals New result on matrix summability factors of infinite series and Fourier series

2019 ◽  
Author(s):  
Şebnem Yıldız
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Factors ◽  
Matrix Summability

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.

On absolute summability factors of infinite series and their application to Fourier series

1967 ◽  
Vol 63 (1) ◽  
pp. 107-118 ◽  
Author(s):  
R. N. Mohapatra ◽  
G. Das ◽  
V. P. Srivastava
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Infinite Series ◽  
Absolute Summability ◽  
Summability Factors ◽  
Partial Sum ◽  
Absolute Summability Factors ◽  
Image Position

Definition. Let {sn} be the n-th partial sum of a given infinite series. If the transformationwhereis a sequence of bounded variation, we say that εanis summable |C, α|.

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 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.

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