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.

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 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 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 Power Increasing Sequences and Their Some New Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Summability Factors ◽  
Power Increasing Sequences ◽  
New Applications ◽  
Weaker Conditions ◽  
Increasing Sequences ◽  
Quasi Power Increasing Sequence

In the work of Bor (2008), we have proved a result dealing with summability factors by using a quasi--power increasing sequence. In this paper, we prove that result under less and more weaker conditions. Some new results have also been obtained.

scholarly journals A new theorem on the absolute Riesz summability factors

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1537-1541 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
General Class ◽  
Summability Factors ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Power Increasing Sequences ◽  
The Absolute ◽  
Increasing Sequences ◽  
Quasi Power Increasing Sequence

In [5], we proved a main theorem dealing with absolute Riesz summability factors of infinite series using a quasi-?-power increasing sequence. In this paper, we generalize that theorem by using a general class of power increasing sequences instead of a quasi-?-power increasing sequence. This theorem also includes some new and known 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 Quasiβ-power increasing sequences

2004 ◽  
Vol 2004 (44) ◽  
pp. 2371-2376 ◽  
Author(s):  
H. Bor ◽  
L. Debnath
Keyword(s):  
Summability Factors ◽  
Power Increasing Sequences ◽  
Weaker Conditions ◽  
Increasing Sequences

We prove a theorem of Mazhar (1999) on|N¯,pn|ksummability factors under weaker conditions by using a quasiβ-power increasing sequence instead of an almost increasing sequence.

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