Factored infinite series and Fourier series involving almost increasing sequences

2021 ◽  
Vol 169 ◽  
pp. 102990
Author(s):  
Hüseyin Bor
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

scholarly journals Quasimonotone and Almost Increasing Sequences and Their New Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
The Absolute ◽  
New Applications ◽  
Weaker Conditions ◽  
Increasing Sequences ◽  
Almost Increasing Sequences ◽  
Absolute Nörlund Summability

Recently, we have proved a main theorem dealing with the absolute Nörlund summability factors of infinite series by using -quasimonotone sequences. In this paper, we prove that result under weaker conditions. A new result has also been obtained.

scholarly journals Almost increasing sequences and their new applications II

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 435-439 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
New Applications ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

In this paper, we generalize a known theorem dealing with |C,?|k summability factors to the |C,?,?,?|k summability factors of infinite series. This theorem also includes some known and new results.

scholarly journals A New Application of Almost Increasing Sequences

2015 ◽  
Vol 61 (1) ◽  
pp. 153-160 ◽  
Author(s):  
H.S. Özarslan ◽  
A. Keten
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
Weaker Conditions ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

Abstract Bor has proved a main theorem dealing with | N̄ , pn|k summability factors of infinite series. In this paper, we have generalized this theorem to the φ − |A, pn|k summability factors, under weaker conditions by using an almost increasing sequence instead of a positive monotonic non-decreasing sequence.

scholarly journals A matrix application of power increasing sequences to infinite series and Fourier series

2020 ◽  
Vol 72 (5) ◽  
Author(s):  
Şebnem Yıldız
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Factors ◽  
Summability Methods ◽  
Matrix Application ◽  
Power Increasing Sequences ◽  
Weaker Conditions ◽  
Increasing Sequences

UDC 517.54 The aim of the paper is a generalization, under weaker conditions, of the main theorem on quasi- σ -power increasing sequences applied to | A , θ n | k summability factors of infinite series and Fourier series. We obtain some new and known results related to basic summability methods.

scholarly journals A new application of almost increasing sequences

2019 ◽  
Vol 18 (1) ◽  
pp. 59-65
Author(s):  
Ahmet Karakaş
Keyword(s):  
Infinite Series ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

Abstract In this paper, a known result dealing with | ̄N, pn|k summability of infinite series has been generalized to the φ − | ̄N, pn; δ|k summability of infinite series by using an almost increasing sequence.

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