scholarly journals The λ ̅-statistically convergent double sequences in fuzzy normed spaces

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 153-163
Author(s):  
Omer Kisi
Keyword(s):  
Double Sequences ◽  
Normed Spaces ◽  
Cauchy Sequences ◽  
Convergent Sequences

We introduce double ? ?-statistically convergent sequences and double ? ?- statistically Cauchy sequences in the fuzzy normed spaces. We study [V,? ?] and [C,1]-summabilities for double sequences. In addition, we obtain the relation between these concepts and ? ?-statistically convergence.

$\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.

Some properties of sequences in gradual normed spaces

2019 ◽  
Vol 13 (04) ◽  
pp. 2050085
Author(s):  
Mina Ettefagh ◽  
Sina Etemad ◽  
Farnaz Y. Azari
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Cauchy Sequences ◽  
Convergent Sequences

In this paper, we investigate some properties of sequences in a gradual normed space. We define some new notions such as gradual convergent sequences, gradual Cauchy sequences, etc., and then we state some theorems about these notions. Finally, in the last section, we bring some illustrative examples.

scholarly journals Statistical convergence of double sequences on probabilistic normed spaces defined by $[ V, \lambda, \mu ]$-summability

2014 ◽  
Vol 33 (2) ◽  
pp. 59-67
Author(s):  
Pankaj Kumar ◽  
S. S. Bhatia ◽  
Vijay Kumar
Keyword(s):  
Statistical Convergence ◽  
Convergence Criteria ◽  
Double Sequences ◽  
Normed Spaces ◽  
Real Numbers ◽  
Positive Real ◽  
Probabilistic Normed Spaces

In this paper, we aim to generalize the notion of statistical convergence for double sequences on probabilistic normed spaces with the help of two nondecreasing sequences of positive real numbers $\lambda=(\lambda_{n})$ and $\mu = (\mu_{n})$  such that each tending to zero, also $\lambda_{n+1}\leq \lambda_{n}+1, \lambda_{1}=1,$ and $\mu_{n+1}\leq \mu_{n}+1, \mu_{1}=1.$ We also define generalized statistically Cauchy double sequences on PN space and establish the Cauchy convergence criteria in these spaces.

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.

Matrix Transformations in an Incomplete Space

1968 ◽  
Vol 20 ◽  
pp. 727-734 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Linear Space ◽  
Cauchy Sequence ◽  
Convergent Sequence ◽  
Convergent Series ◽  
Matrix Transformations ◽  
Cauchy Sequences ◽  
Complex Linear ◽  
Incomplete Space ◽  
Bounded Sequences ◽  
Convergent Sequences

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences.

scholarly journals Lacunary Statistical Delta 2 2-Quasi Cauchy Double Sequences

2021 ◽  
Vol 09 (06) ◽  
Author(s):  
A. G. K. Ali ◽  
Keyword(s):  
Double Sequences ◽  
Cauchy Sequences

In this paper, we have introduced the extension of recently introduced notion of summability of lacunary statistical delta 2 quasi Cauchy sequences to double sequences and established some essential results using analogy.

I_2-LOCALIZED DOUBLE SEQUENCES IN METRIC SPACES

2021 ◽  
Vol 10 (6) ◽  
pp. 2877-2885
Author(s):  
C. Granados ◽  
J. Bermúdez
Keyword(s):  
Metric Spaces ◽  
The Other ◽  
Double Sequences ◽  
Other Hand ◽  
Cauchy Sequences

In this article, the notions of $ I_{2} $-localized and $ I_{2}^{*} $-localized sequences in metric spaces are defined. Besides, we study some properties associated to $ I_{2} $-localized and $ I_{2} $-Cauchy sequences. On the other hand, we define the notion of uniformly $ I_{2} $-localized sequences in metric spaces.

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