An application of quasi-monotone sequences to infinite series and Fourier series

2017 ◽  
Vol 8 (1) ◽  
pp. 77-83
Author(s):  
Hüseyin Bor
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Monotone 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.

scholarly journals On quasi-monotone sequences and their applications

1991 ◽  
Vol 43 (2) ◽  
pp. 187-192 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Factors ◽  
Monotone Sequences

In this paper using δ-quasi-monotone sequences a theorem on summability factors of infinite series, which generalises a theorem of Mazhar [7] on |C, 1|k summability factors of infinite series, is proved. Also we apply the theorem to Fourier series.

A new application of quasi monotone sequences and quasi power increasing sequences to factored infinite series

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5105-5109
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
Monotone Sequences ◽  
Power Increasing Sequences ◽  
Weaker Conditions ◽  
Increasing Sequences

In this paper, we generalize a known theorem under more weaker conditions dealing with the generalized absolute Ces?ro summability factors of infinite series by using quasi monotone sequences and quasi power increasing sequences. This theorem also includes some new results.

On the Absolute Nörlund Summability of a Fourier Series

1973 ◽  
Vol 16 (4) ◽  
pp. 599-602
Author(s):  
D. S. Goel ◽  
B. N. Sahney
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Infinite Series ◽  
Partial Sums ◽  
The Absolute ◽  
Image Position ◽  
Absolute Nörlund Summability

Let be a given infinite series and {sn} the sequence of its partial sums. Let {pn} be a sequence of constants, real or complex, and let us write(1.1)If(1.2)as n→∞, we say that the series is summable by the Nörlund method (N,pn) to σ. The series is said to be absolutely summable (N,pn) or summable |N,pn| if σn is of bounded variation, i.e.,(1.3)

Transformation of Fourier Series by Means of General Monotone Sequences

2020 ◽  
Vol 107 (5-6) ◽  
pp. 740-758
Author(s):  
A. A. Jumabayeva ◽  
B. V. Simonov
Keyword(s):  
Fourier Series ◽  
Monotone Sequences

scholarly journals Absolute summability of a fourier series and its derived series by a product method

1972 ◽  
Vol 14 (4) ◽  
pp. 470-481 ◽  
Author(s):  
H. P. Dikshit
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Absolute Summability ◽  
Partial Sums ◽  
Product Method ◽  
Derived Series

Let Σan be a given infinite series with the sequence of partial sums {Sn}. Let {Pn} be a sequence of constants, real or complex, and let us write Pn = p0 + p1 + … + pn; P-1 = P-1 = 0.

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