scholarly journals Different behaviors of rough weighted statistical limit set under unbounded moduli

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2583-2600
Author(s):  
Sanjoy Ghosal ◽  
Sumit Som
Keyword(s):  
Limit Set ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Cluster Points

In this paper we introduce f-rough weighted statistical limit set and f-weighted statistical cluster points set which are natural generalizations of rough statistical limit set and f-statistical cluster points set of sequence respectively. Some new examples are constructed to ensure the deviation of basic results. So both the sets don?t follow the nature of usual extension properties which will be discussed here.

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.

scholarly journals Effects on rough I-lacunary statistical convergence to induce the weighted sequence

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3557-3568 ◽  
Author(s):  
Sanjoy Ghosal ◽  
Mandobi Banerjee
Keyword(s):  
Statistical Convergence ◽  
Limit Set ◽  
Topological Approach ◽  
Weighted Sequence ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Lacunary Statistical Convergence ◽  
Cluster Points

Two classes of sets are introduced: rough weighted I-lacunary statistical limit set and weighted I-lacunary statistical cluster points set which are natural generalizations of rough I-limit set and I-cluster points set respectively. To highlight the variation from basic results we place into some new examples. So our aim is to analyze the different behaviors of the new convergences and characterize both the sets with topological approach like closedness, boundedness, compactness etc.

Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space

2020 ◽  
Vol 70 (3) ◽  
pp. 667-680
Author(s):  
Sanjoy Ghosal ◽  
Avishek Ghosh
Keyword(s):  
Metric Space ◽  
Limit Set ◽  
Positive Real ◽  
Weighted Sequence ◽  
Statistical Limit ◽  
Lacunary Statistical Convergence ◽  
Natural Density ◽  
Limit Points ◽  
Cluster Points

AbstractIn 2018, Das et al. [Characterization of rough weighted statistical statistical limit set, Math. Slovaca 68(4) (2018), 881–896] (or, Ghosal et al. [Effects on rough 𝓘-lacunary statistical convergence to induce the weighted sequence, Filomat 32(10) (2018), 3557–3568]) established the result: The diameter of rough weighted statistical limit set (or, rough weighted 𝓘-lacunary limit set) of a sequence x = {xn}n∈ℕ is $\begin{array}{} \frac{2r}{{\liminf\limits_{n\in A}} t_n} \end{array}$ if the weighted sequence {tn}n∈ℕ is statistically bounded (or, self weighted 𝓘-lacunary statistically bounded), where A = {k ∈ ℕ : tk < M} and M is a positive real number such that natural density (or, self weighted 𝓘-lacunary density) of A is 1 respectively. Generally this set has no smaller bound other than $\begin{array}{} \frac{2r}{{\liminf\limits_{n\in A}} t_n} \end{array}$. We concentrate on investigation that whether in a θ-metric space above mentioned result is satisfied for rough weighted 𝓘-limit set or not? Answer is no. In this paper we establish infinite as well as unbounded θ-metric space (which has not been done so far) by utilizing some non-trivial examples. In addition we introduce and investigate some problems concerning the sets of rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space and formalize how these sets could deviate from the existing basic 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

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.

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