scholarly journals ON $\mathcal{I}_2$-CONVERGENCE AND $\mathcal{I}_2$-CAUCHY DOUBLE SEQUENCES OF FUNCTIONS IN 2-NORMED SPACES

2020 ◽  
pp. 801
Author(s):  
Sevim Yegül ◽  
Erdinç Dündar
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Double Sequences ◽  
Normed Spaces

In this study, firstly, we studied some properties of $\mathcal{I}_2$-convergence. Then, we introduced $\mathcal{I}_2$-Cauchy and $\mathcal{I}_2^*$-Cauchy sequence of double sequences of functions in $2$-normed space. Also, were investigated relationships between them for double sequences of functions in $2$-normed spaces.

scholarly journals Ideal Convergence and Completeness of a Normed Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 897 ◽  
Author(s):  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
María del Pilar Romero de la Rosa ◽  
Antonio Sala
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Convergence Space ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Underlying Space ◽  
Phd Thesis

We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.

scholarly journals Strongly Lacunary Ward Continuity in 2-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hüseyin Çakalli ◽  
Sibel Ersan
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Cauchy Sequences

A functionfdefined on a subsetEof a 2-normed spaceXis strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points inE; that is,(f(xk))is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.

scholarly journals New Fuzzy Normed Spaces

2012 ◽  
Vol 9 (3) ◽  
pp. 559-564 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Continuous Convergence ◽  
Definition Of

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

scholarly journals Ideally Statistical Convergence in n-normed Space

2020 ◽  
pp. 75-84
Author(s):  
Nazneen Khan ◽  
Amani Shatarah
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Topological Properties ◽  
Normed Spaces

The aim of the article is to extend the concept of Ideally statistical convergence from 2 normed spaces to n-normed space. We have also study and prove some important algebraic and topological properties of Ideally-statistical convergence of real sequences in n-normed space. In the last part of this article we obtain a criterion for I-statistically Cauchy sequence in n-normed space to be I-statistically Cauchy with respect to ∥.∥∞.

scholarly journals Classes ofI-Convergent Double Sequences overn-Normed Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Nazneen Khan
Keyword(s):  
Normed Space ◽  
Topological Properties ◽  
Double Sequences ◽  
Normed Spaces ◽  
Inclusion Relations

I introduce some new classes ofI-convergent double sequences defined by a sequence of moduli overn-normed space. Study of their algebraic and topological properties and some inclusion relations has also been done.

scholarly journals A variation on strongly lacunary delta ward continuity in 2-normed spaces

2019 ◽  
Vol 38 (7) ◽  
pp. 195-202
Author(s):  
Sibel Ersan
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Cauchy Sequences

A sequence $(x_{k})$ of points in a subset E of a 2-normed space $X$ is called strongly lacunary $\delta$-quasi-Cauchy, or $N_\theta$-$\delta$-quasi-Cauchy if $(\Delta x_k)$ is $N_\theta$-convergent to 0, that is $\lim_{r\rightarrow\infty}\frac{1}{h_r}\sum_{k\in I_r}||\Delta^2 x_k, z||=0$ for every fixed $z\in X$. A function defined on a subset $E$ of $X$ is called strongly lacunary $\delta$-ward continuous if it preserves  $N_{\theta}$-$\delta$-quasi-Cauchy sequences, i.e. $(f(x_{k}))$ is an $N_{\theta}$-$\delta$-quasi-Cauchy sequence whenever $(x_{k})$ is. In this study we obtain some theorems related to strongly lacunary $\delta$-quasi-Cauchy sequences.

$\bar \lambda $-statistically convergent double sequences in probabilistic normed spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
E. Savaş ◽  
S. Mohiuddine
Keyword(s):  
Normed Space ◽  
Double Sequences ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Probabilistic Normed Spaces ◽  
Cauchy Sequences

AbstractThe purpose of this paper is to introduce and study the concepts of double $\bar \lambda $-statistically convergent and double $\bar \lambda $-statistically Cauchy sequences in probabilistic normed space.

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 Pringsheim and statistical convergence for double sequences on $ L- $fuzzy normed space

2021 ◽  
Vol 6 (12) ◽  
pp. 13726-13733
Author(s):  
Reha Yapalı ◽  
◽  
Utku Gürdal ◽  
Keyword(s):  
Normed Space ◽  
Statistical Convergence ◽  
Double Sequences ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Classical Sense

<abstract><p>In this paper, we study the concept of statistical convergence for double sequences on $ L- $fuzzy normed spaces. Then we give a useful characterization on the statistical convergence of double sequences with respect to their convergence in the classical sense and we illustrate that our method of convergence is weaker than the usual convergence for double sequences on $ L- $fuzzy normed spaces.</p></abstract>

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