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.

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 Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Double Sequence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Lacunary Statistical Convergence ◽  
Cesaro Convergence

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

scholarly journals Unconditionally converging polynomials on Banach spaces

1995 ◽  
Vol 117 (2) ◽  
pp. 321-331 ◽  
Author(s):  
Manuel Gonz´lez ◽  
Joaquín M. Gutiérrez
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Weak Topology ◽  
Linear Operators ◽  
Null Sequence ◽  
Good Tool ◽  
Image Position ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series

In the study of polynomials acting on Banach spaces, the weak topology is not such a good tool as in the case of linear operators, due to the bad behaviour of the polynomials with respect to the weak convergence. For example,is a continuous polynomial taking a weakly null sequence into a sequence having no weakly Cauchy subsequences. In this paper we show that the situation is not so bad for unconditional series. Recall that is a weakly unconditionally Cauchy series (in short a w.u.C. series) in a Banach space E if for every f ε E* we have that and is an unconditionally converging series (in short an u.c. series) if every subseries is norm convergent.

scholarly journals ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

2021 ◽  
pp. 435
Author(s):  
Ömer Kişi
Keyword(s):  
Normed Space ◽  
Statistical Convergence ◽  
Double Sequences ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
New Methods ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Lacunary Statistical Convergence ◽  
Intuitionistic Fuzzy Normed Spaces

In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.

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.

Lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed space

2014 ◽  
Vol 26 (3) ◽  
pp. 1289-1299
Author(s):  
Vatan Karakaya ◽  
Necip Simsek ◽  
Faik Gürsoy ◽  
Müzeyyen Ertürk
Keyword(s):  
Normed Space ◽  
Statistical Convergence ◽  
Fuzzy Normed Space ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences

ON LACUNARY STATISTICAL CONVERGENCE AND SOME PROPERTIES IN FUZZY N-NORMED SPACES

2018 ◽  
Vol 7 (3) ◽  
pp. 1
Author(s):  
RECAİ TÜRKMEN MUHAMMED ◽  
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Lacunary Statistical Convergence
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