scholarly journals A summability factor theorem for a generalized absolute Cesàro summability

2011 ◽  
Vol 53 (5-6) ◽  
pp. 832-838 ◽  
Author(s):  
Dansheng Yu ◽  
Guanzhen Zhou
Keyword(s):  
Cesàro Summability ◽  
Summability Factor ◽  
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.

A summability factor theorem and applications

2004 ◽  
Vol 153 (1) ◽  
pp. 155-163
Author(s):  
B.E. Rhoades ◽  
Ekrem Savaş
Keyword(s):  
Summability Factor ◽  
Factor Theorem
Sign in / Sign up

Export Citation Format

Share Document