scholarly journals Completeness of a normed space via strong p-Cesàro summability

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3013-3022 ◽  
Author(s):  
F. Léon-Saavedra ◽  
S. Moreno-Pulido ◽  
A. Sala-Pérez
Keyword(s):  
Normed Space ◽  
Convergent Series ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Weakly Unconditionally Cauchy Series ◽  
Unconditionally Convergent Series ◽  
Cauchy Series

In this paper we will characterize the completeness and barrelledness of a normed space through the strong p-Ces?ro summability of series. A new characterization of weakly unconditionally Cauchy series and unconditionally convergent series through the strong p-Ces?ro summability is obtained.

scholarly journals Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1066 ◽  
Author(s):  
Soledad Moreno-Pulido ◽  
Giuseppina Barbieri ◽  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
Antonio Sala-Pérez
Keyword(s):  
Banach Space ◽  
Normed Space ◽  
Statistical Convergence ◽  
Lacunary Statistical Convergence ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series ◽  
Cesaro Convergence

In this manuscript we characterize the completeness of a normed space through the strong lacunary ( N θ ) and lacunary statistical convergence ( S θ ) of series. A new characterization of weakly unconditionally Cauchy series through N θ and S θ is obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesàro convergence summability space.

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.

scholarly journals Unconditionally Cauchy series and Cesàro summability

2006 ◽  
Vol 324 (1) ◽  
pp. 39-48 ◽  
Author(s):  
A. Aizpuru ◽  
A. Gutiérrez-Dávila ◽  
A. Sala
Keyword(s):  
Cesàro Summability ◽  
Cesaro Summability ◽  
Cauchy Series

scholarly journals On compact operators on some spaces related to matrix B(r, s)

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 41-51 ◽  
Author(s):  
Ivana Djolovic
Keyword(s):  
Compact Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Subject Classifications ◽  
Mathematics Subject Classifications

Many sequence spaces arise from different concepts of summability. Recent results obtained by Altay, Ba?ar and Malkowsky [2] are related to strong Cesaro summability and boundedness. They determined ?-duals of the new sequence spaces and characterized some classes of matrix transformations on them. Here, we will present new results supplementing their research with the characterization of classes of compact operators on those spaces. 2010 Mathematics Subject Classifications. 46B15, 46B45, 46B50. .

scholarly journals Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kuldip Raj ◽  
Swati Jasrotia ◽  
M. Mursaleen
Keyword(s):  
Normed Space ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Almost Convergence ◽  
Weighted Mean ◽  
Fractional Difference ◽  
Weakly Unconditionally Cauchy Series ◽  
Vector Valued ◽  
Cauchy Series

AbstractIn this study, we deal with some new vector valued multiplier spaces $S_{G_{h}}(\sum_{k}z_{k})$ S G h ( ∑ k z k ) and $S_{wG_{h}}(\sum_{k}z_{k})$ S w G h ( ∑ k z k ) related with $\sum_{k}z_{k}$ ∑ k z k in a normed space Y. Further, we obtain the completeness of these spaces via weakly unconditionally Cauchy series in Y and $Y^{*}$ Y ∗ . Moreover, we show that if $\sum_{k}z_{k}$ ∑ k z k is unconditionally Cauchy in Y, then the multiplier spaces of $G_{h}$ G h -almost convergence and weakly $G_{h}-$ G h − almost convergence are identical. Finally, some applications of the Orlicz–Pettis theorem with the newly formed sequence spaces and unconditionally Cauchy series $\sum_{k}z_{k}$ ∑ k z k in Y are given.

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.

scholarly journals Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

2000 ◽  
Vol 50 (4) ◽  
pp. 889-896 ◽  
Author(s):  
F. J. Pérez-Fernández ◽  
F. Benitez-Trujillo ◽  
A. Aizpuru
Keyword(s):  
Normed Spaces ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series
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