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 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.

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.

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 An application of almost increasing sequences

2000 ◽  
Vol 23 (12) ◽  
pp. 859-863 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Summability Factors ◽  
Weaker Conditions ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

We extended a theorem of Mishra and Srivastava (1983–1984) on|C,1|ksummability factors, using almost increasing sequences, to|N¯,pn|ksummability under weaker conditions.

scholarly journals On almost increasing sequences and its applications

2001 ◽  
Vol 25 (5) ◽  
pp. 293-298 ◽  
Author(s):  
Hikmet S. Özarslan
Keyword(s):  
General Theorem ◽  
Summability Factors ◽  
Weaker Conditions ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

We prove a general theorem on|N¯,pn;δ|ksummability factors, which generalizes a theorem of Bor (1994) on|N¯,pn|ksummability factors, under weaker conditions by using an almost increasing sequence.

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 On an application of almost increasing sequences

2001 ◽  
Vol 27 (1) ◽  
pp. 7-15 ◽  
Author(s):  
Hüseyın Bor
Keyword(s):  
Summability Factors ◽  
Alpha Beta ◽  
Weaker Conditions ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

Using an almost increasing sequence, a result of Mazhar (1977) on|C,1|ksummability factors has been generalized for|C,α;β|kand|N¯,pn;β|ksummability factors under weaker conditions.

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.

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