A new factor theorem on generalized absolute Cesàro summability

2020 ◽  
pp. 1-6 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Cesàro Summability ◽  
Cesaro Summability ◽  
Factor Theorem

Summability methods which include the Riesz typical means. II

1971 ◽  
Vol 69 (2) ◽  
pp. 297-300 ◽  
Author(s):  
B. C. Russell
Keyword(s):  
Regular Sequence ◽  
Cesàro Summability ◽  
Convergence Factor ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Factor Theorem ◽  
T Matrix ◽  
Image Position ◽  
Summability Matrix ◽  
Necessary And Sufficient

By making use of a convergence-factor theorem of Bosanquet(3), Cooke((4), Theorem I) gave conditions for a regular sequence-to-sequence summability matrix B to be at least as strong as Cesàro summability (C, κ) (κ > 0), namely:Theorem C. Let κ > 0. In order that the T-matrix B = (bρμ) shall satisfy B ⊇ (C, κ) it is necessary and sufficient thatIf 0 < κ ≤ 1 then (2) alone is necessary and sufficient.

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.

scholarly journals Lebesgue points of $$\ell _1$$-Cesàro summability of d-dimensional Fourier series

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Lebesgue Point ◽  
Cesàro Means ◽  
Cesàro Summability ◽  
Cesaro Means ◽  
Cesaro Summability ◽  
Lebesgue Points ◽  
Cesáro Means

AbstractWe generalize the classical Lebesgue’s theorem and prove that the $$\ell _1$$ ℓ 1 -Cesàro means of the Fourier series of the multi-dimensional function $$f\in L_1({{\mathbb {T}}}^d)$$ f ∈ L 1 ( T d ) converge to f at each strong $$\omega $$ ω -Lebesgue point.

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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