$\mathcal{I}$-statistical limit points and $\mathcal{I}$-statistical cluster points in Probabilistic Normed Spaces

2020 ◽  
Vol Accepted ◽  
Author(s):  
Argha Ghosh ◽  
Samiran Das
Keyword(s):  
Normed Spaces ◽  
Statistical Cluster ◽  
Probabilistic Normed Spaces ◽  
Statistical Limit ◽  
Limit Points ◽  
Cluster Points

scholarly journals On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Pratulananda Das ◽  
Kaustubh Dutta ◽  
Vatan Karakaya
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Statistical Cluster ◽  
Probabilistic Normed Spaces ◽  
Extremal Limit ◽  
Limit Points ◽  
Appl Math ◽  
Cluster Points

We consider the recently introduced notion ofℐ-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strongℐ-statistical cluster points and extremal limit points, and strongℐ-statistical continuity and strongℐ-statisticalD-boundedness in probabilistic normed spaces and study some of their important properties.

scholarly journals Lacunary Statistical Limit Points in Random 2-Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
A. Güncan ◽  
U. Yamancı ◽  
M. Gürdal
Keyword(s):  
Normed Spaces ◽  
Statistical Limit ◽  
Limit Points ◽  
Cluster Points

We introduce the notion θ-cluster points, investigate the relation between θ-cluster points and limit points of sequences in the topology induced by random 2-normed spaces, and prove some important results.

scholarly journals New Results on I 2 -Statistically Limit Points and I 2 -Statistically Cluster Points of Sequences of Fuzzy Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ö. Kişi ◽  
M. B. Huban ◽  
M. Gürdal
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Double Sequence ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Number Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points ◽  
The Relationship ◽  
Cluster Points

In this paper, some existing theories on convergence of fuzzy number sequences are extended to I 2 -statistical convergence of fuzzy number sequence. Also, we broaden the notions of I -statistical limit points and I -statistical cluster points of a sequence of fuzzy numbers to I 2 -statistical limit points and I 2 -statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all I 2 -statistical cluster points and the set of all I 2 -statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.

scholarly journals Lacunary Statistical Limit and Cluster Points of Generalized Difference Sequences of Fuzzy Numbers

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Pankaj Kumar ◽  
Vijay Kumar ◽  
S. S. Bhatia
Keyword(s):  
Fuzzy Numbers ◽  
Difference Sequences ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Inclusion Relations ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points ◽  
Cluster Points

The aim of present work is to introduce and study lacunary statistical limit and lacunary statistical cluster points for generalized difference sequences of fuzzy numbers. Some inclusion relations among the sets of ordinary limit points, statistical limit points, statistical cluster points, lacunary statistical limit points, and lacunary statistical cluster points for these type of sequences are obtained.

scholarly journals I-statistical limit points and I-statistical cluster points

2019 ◽  
Vol 38 (5) ◽  
pp. 1011-1026
Author(s):  
Prasanta Malik ◽  
Argha Ghosh ◽  
Samiran Das
Keyword(s):  
Statistical Cluster ◽  
Statistical Limit ◽  
Limit Points ◽  
Cluster Points

SOME PROPERTIES OF EQUIDISTRIBUTED AND WELL DISTRIBUTED SEQUENCES

2021 ◽  
Vol 10 (9) ◽  
pp. 3175-3184
Author(s):  
Leila Miller-Van Wieren
Keyword(s):  
Real Numbers ◽  
Statistical Cluster ◽  
Different Types ◽  
Limit Points ◽  
Cluster Points

Many authors studied properties related to distribution and summability of sequences of real numbers. In these studies, different types of limit points of a sequence were introduced and studied including statistical and uniform statistical cluster points of a sequence. In this paper, we aim to prove some new results about the nature of different types of limit points, this time connected to equidistributed and well distributed sequences.

scholarly journals On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Normed Space ◽  
Complex Numbers ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Cauchy Sequences ◽  
Limit Points ◽  
Positive Integers ◽  
Cluster Points

An idealIis a hereditary and additive family of subsets of positive integersℕ. In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points. Furthermore, Cauchy andIL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

scholarly journals On rough convergence in 2-normed spaces and some properties

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5077-5086
Author(s):  
Mukaddes Arslan ◽  
Erdinç Dündar
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Fixed Sequence ◽  
Limit Points ◽  
Cluster Points

In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-normed space. Also, we examined the dependence of r-limit LIMr 2xn of a fixed sequence (xn) on varying parameter r in 2-normed space

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