scholarly journals Statistical cluster point and statistical limit point sets of subsequences of a given sequence

2020 ◽  
pp. 1-4
Author(s):  
Harry I. MİLLER ◽  
Leila Miller-van WİEREN
Keyword(s):  
Limit Point ◽  
Cluster Point ◽  
Point Sets ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Statistical Cluster Point

scholarly journals Statistical convergence of double sequences in fuzzy normed spaces

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 673-681 ◽  
Author(s):  
S.A. Mohiuddine ◽  
H. Şevli ◽  
M. Cancan
Keyword(s):  
Limit Point ◽  
General Class ◽  
Statistical Convergence ◽  
Cluster Point ◽  
Double Sequences ◽  
Normed Spaces ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Statistical Cluster Point ◽  
The Relationship

In this paper, we study the concepts of statistically convergent and statistically Cauchy double sequences in the framework of fuzzy normed spaces which provide better tool to study a more general class of sequences. We also introduce here statistical limit point and statistical cluster point for double sequences in this framework and discuss the relationship between them.

Rough statistical cluster points

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5295-5304
Author(s):  
Salih Aytar
Keyword(s):  
Statistical Convergence ◽  
Cluster Point ◽  
Convergence Criteria ◽  
Finite Dimensional ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Condensation Point ◽  
Statistical Cluster Point ◽  
Dimensional Normed Space ◽  
Cluster Points

In this paper, we define the concepts of rough statistical cluster point and rough statistical limit point of a sequence in a finite dimensional normed space. Then we obtain an ordinary statistical convergence criteria associated with rough statistical cluster point of a sequence. Applying these definitions to the sequences of functions, we come across a new concept called statistical condensation point. Finally, we observe the relations between the sets of statistical condensation points, rough statistical cluster points and rough statistical limit points of a sequence of functions.

Some further studies on strong ℐλ-statistical convergence in probabilistic metric spaces

Analysis ◽  
2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Argha Ghosh ◽  
Samiran Das
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Cluster Point ◽  
Probabilistic Metric Spaces ◽  
Basic Properties ◽  
Statistical Cluster ◽  
Cauchy Sequences ◽  
Convergence Of Sequences ◽  
Statistical Cluster Point ◽  
Probabilistic Metric

Abstract We prove some basic properties of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence of sequences in probabilistic metric spaces and introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical cluster point. We also introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences in probabilistic metric spaces. Further, we establish a connection between strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence and strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences.

scholarly journals Statistical limit point theorems

2000 ◽  
Vol 23 (11) ◽  
pp. 741-752 ◽  
Author(s):  
Jeff Zeager
Keyword(s):  
Complex Number ◽  
Limit Point ◽  
Statistical Convergence ◽  
Nonnegative Matrix ◽  
Bounded Sequence ◽  
Regular Matrix ◽  
Number Sequence ◽  
Statistical Limit ◽  
Limit Points

It is known that given a regular matrixAand a bounded sequencexthere is a subsequence (respectively, rearrangement, stretching)yofxsuch that the set of limit points ofAyincludes the set of limit points ofx. Using the notion of a statistical limit point, we establish statistical convergence analogues to these results by proving that every complex number sequencexhas a subsequence (respectively, rearrangement, stretching)ysuch that every limit point ofxis a statistical limit point ofy. We then extend our results to the more generalA-statistical convergence, in whichAis an arbitrary nonnegative matrix.

When deviation happens between rough statistical convergence and rough weighted statistical convergence

2019 ◽  
Vol 69 (4) ◽  
pp. 871-890 ◽  
Author(s):  
Sanjoy Ghosal ◽  
Avishek Ghosh
Keyword(s):  
Statistical Convergence ◽  
Limit Set ◽  
Double Sequences ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Cluster Points

Abstract In this paper we introduce rough weighted statistical limit set and weighted statistical cluster points set which are natural generalizations of rough statistical limit set and statistical cluster points set of double sequences respectively. Some new examples are constructed to ensure the deviation of basic results. Both the sets don’t follow the usual extension properties which will be discussed here.

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