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.

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.

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 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

Summability factors for Riesz loǵarithmic means of order one for a Fourier series

1970 ◽  
Vol 67 (2) ◽  
pp. 307-320
Author(s):  
R. N. Mohapatra
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Factors ◽  
Partial Sum ◽  
Logarithmic Means ◽  
Image Position

Let 0 < λ1 < λ2 < … < λn → ∞ (n→∞). We writeLet ∑an be a given infinite series with the sequence {sn} for its nth partial sum. The (R, λ, 1) mean of the sequence {sn} is given by

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.

scholarly journals Absolute Riesz summability factors for Fourier series

1970 ◽  
Vol 17 (1) ◽  
pp. 65-70
Author(s):  
Prem Chandra
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Factors ◽  
Monotonic Sequence ◽  
Riesz Mean ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Image Position

Let ∑an be a given infinite series and {λn} a non-negative, strictly increasing, monotonic sequence, tending to infinity with n. We write, for w > λ0,and, for r>0, we write is known as the Riesz sum of “ type ” λn and “ order ” r, andis called the Riesz mean of type λn and order r.

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