scholarly journals A NEW STUDY ON ABSOLUTE CESÀRO SUMMABILITY FACTORS

2021 ◽  
pp. 1199
Author(s):  
Huseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Method ◽  
Summability Factors ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Alpha Beta ◽  
Weaker Conditions

In this paper, we have generalized a known theorem dealing with $\varphi-{\mid{C},\alpha,\mid}_k$ summability factors of infinite series to the $\varphi-{\mid{C},\alpha,\beta\mid}_k$ summability method under weaker conditions. Also, some new and known results are obtained.

scholarly journals Factors for absolute Cesaro summability

2001 ◽  
Vol 32 (1) ◽  
pp. 21-25
Author(s):  
A. Nihal Tuncer
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
Cesàro Summability ◽  
Monotone Sequences ◽  
Cesaro Summability ◽  
Alpha Beta

In this paper using $ \delta $-quasi-monotone sequences a theorem on $ | C, \alpha, \beta; \delta |_k $ summability factors of infinite series, which generalizes a theorem of Mazhar[6] on $ | C, 1 |_k $ summability factors, has been proved.

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.

On Generalized Absolute Cesàro Summability

2011 ◽  
Vol 57 (2) ◽  
pp. 323-328 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Summability Factors ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Weaker Conditions

On Generalized Absolute Cesàro SummabilityIn this paper, a main theorem dealing with |C, 1 |ksummability factors has been generalized under more weaker conditions for |C, α, β |ksummability factors. This theorem also includes some new results.

scholarly journals On the absolute Cesaro summability factors of trigonometric series

1968 ◽  
Vol 16 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Niranjan Singh
Keyword(s):  
Trigonometric Series ◽  
Infinite Series ◽  
Summability Factors ◽  
Cesàro Summability ◽  
Partial Sum ◽  
Cesaro Summability ◽  
The Absolute ◽  
Image Position

Let be any given infinite series with sn as its n-th partial sum.We writeandwhere

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.

Some sequence spaces and completeness of normed spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 281-287
Author(s):  
RAMAZAN KAMA ◽  
◽  
BILAL ALTAY ◽  
Keyword(s):  
Normed Space ◽  
Summability Method ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Cesàro Summability ◽  
Cesaro Summability

In this paper we introduce new sequence spaces obtained by series in normed spaces and Cesaro summability method. We prove that completeness ´ and barrelledness of a normed space can be characterized by means of these sequence spaces. Also we establish some inclusion relationships associated with the aforementioned sequence spaces.

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