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 On Probabilistic Alpha-Fuzzy Fixed Points and Related Convergence Results in Probabilistic Metric and Menger Spaces under Some Pompeiu-Hausdorff-Like Probabilistic Contractive Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Convergence Results ◽  
Menger Spaces ◽  
Convergence Of Sequences ◽  
Probabilistic Metric

In the framework of complete probabilistic metric spaces and, in particular, in probabilistic Menger spaces, this paper investigates some relevant properties of convergence of sequences to probabilisticα-fuzzy fixed points under some types of probabilistic contractive conditions.

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.

scholarly journals On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Pratulananda Das ◽  
Kaustubh Dutta ◽  
Vatan Karakaya ◽  
Sanjoy Ghosal
Keyword(s):  
Strong Convergence ◽  
Metric Space ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Strong Topology ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
New Approach ◽  
Lacunary Statistical Convergence ◽  
Probabilistic Metric

Following the line of (Das et al., 2011, Savas and Das, 2011), we make a new approach in this paper to extend the notion of strong convergence and more general strong statistical convergence (Şençimen and Pehlivan, 2008) using ideals and introduce the notion of strongℐ- andℐ*-statistical convergence and two related concepts, namely, strongℐ-lacunary statistical convergence and strongℐ-λ-statistical convergence in a probabilistic metric space endowed with strong topology. We mainly investigate their interrelationship and study some of their important properties.

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.

scholarly journals Some fixed point results in a strong probabilistic metric spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2201-2209 ◽  
Author(s):  
Danijela Karaklic ◽  
Ljiljana Gajic ◽  
Nebojsa Ralevic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Basic Properties ◽  
Contractive Type ◽  
Probabilistic Metric

In this paper we introduced the concept of strong probabilistic metric spaces (sPM spaces) and we show some of its basic properties. In this frame we present several fixed point results for mappings of contractive type. Our results generalize and unify several fixed point theorems in literature. Finally, we give some possible applications of our results.

scholarly journals Strongly $\lambda$-Statistically and Strongly Vallée-Poussin Pre-Cauchy Sequences in Probabilistic Metric Spaces

2021 ◽  
Vol 53 ◽  
Author(s):  
Argha Ghosh ◽  
Samiran Das
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Strong Topology ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
Cauchy Sequences ◽  
Probabilistic Metric ◽  
Convergent Sequences

We introduce the notions of strongly $\lambda$-statistically pre-Cauchy and strongly Vall´ee-Poussin pre-Cauchy sequences in probabilistic metric spaces endowed with strong topology. And we show that these two new notions are equivalent. Strongly $\lambda$-statistically convergent sequences are strongly $\lambda$-statistically pre-Cauchy sequences, and we give an example to show that there is a sequence in a probabilistic metric space which is strongly $\lambda$-statistically pre-Cauchy but not strongly $\lambda$-statistically convergent.

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