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.

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 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.

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 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 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

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 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 factor theorem on absolute matrix summability method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Şebnem Yıldız
Keyword(s):  
Infinite Series ◽  
Summability Method ◽  
Summability Factor ◽  
Matrix Summability ◽  
Absolute Matrix Summability ◽  
Matrix Generalization ◽  
Summability Methods ◽  
Power Increasing Sequences ◽  
Factor Theorem ◽  
Increasing Sequences

Abstract In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods

scholarly journals A new factor theorem for generalized Cesàro summability

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1205-1209
Author(s):  
Hüseyin Bor
Keyword(s):  
Cesàro Summability ◽  
Cesaro Summability ◽  
Power Increasing Sequences ◽  
Factor Theorem ◽  
Weaker Conditions ◽  
Increasing Sequences

In [6], we proved a theorem dealing with an application of quasi-f-power increasing sequences. In this paper, we prove that theorem under less and weaker conditions. This theorem also includes several new results.

Sign in / Sign up

Export Citation Format

Share Document