On statistical convergence in fuzzy metric spaces

2020 ◽  
Vol 39 (3) ◽  
pp. 3987-3993
Author(s):  
Changqing Li ◽  
Yanlan Zhang ◽  
Jing Zhang
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Active Area ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Cauchy Sequences ◽  
Convergent Sequences

The idea of statistical convergence, which was first introduced by Fast and Steinhaus independently in 1951, has become one of the most active area of research in the field of mathematics. Recently, it has been applied to the realm of metrics by several authors and some useful results have been obtained. However, the existence of non-completable fuzzy metric spaces, in the sense of George and Veeramani, demonstrates that the theory of fuzzy metrics seem to be richer than that of metrics. In view of this, we attempt to generalize this convergence to the realm of fuzzy metrics. Firstly, we introduce the concept of sts-convergence in fuzzy metric spaces. Then we characterize those fuzzy metric spaces in which all convergent sequences are sts-convergent. Finally, we study sts-Cauchy sequences in fuzzy metric spaces and sts-completeness of fuzzy metric spaces.

scholarly journals Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Double Sequence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Lacunary Statistical Convergence ◽  
Cesaro Convergence

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

scholarly journals Lacunary ℐ -Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mualla Birgül Huban
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Ideal Convergence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
New Type

The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the lacunary ℐ -invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces (briefly, IFMS). In this study, we examine the notions of lacunary ℐ -invariant convergence W ℐ σ θ η , ν (Wijsman sense), lacunary ℐ ∗ -invariant convergence W ℐ σ θ ∗ η , ν (Wijsman sense), and q -strongly lacunary invariant convergence W N σ θ η , ν q (Wijsman sense) of sequences of sets in IFMS. Also, we give the relationships among Wijsman lacunary invariant convergence, W N σ θ η , ν q , W ℐ σ θ η , ν , and W ℐ σ θ ∗ η , ν in IFMS. Furthermore, we define the concepts of W ℐ σ θ η , ν -Cauchy sequence and W ℐ σ θ ∗ η , ν -Cauchy sequence of sets in IFMS. Furthermore, we obtain some features of the new type of convergences in IFMS.

sp− Closedness and sp − Convergent Sequences in Intuitionistic Fuzzy Metric Space

2021 ◽  
Author(s):  
vakeel A. khan ◽  
MOBEEN AHMAD ◽  
Izhar Ali khan
Keyword(s):  
Present Article ◽  
Metric Space ◽  
Metric Spaces ◽  
Convergent Sequence ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Closed Sets ◽  
Intuitionistic Fuzzy ◽  
Convergent Sequences

Abstract The aim of present article is to introduce the concepts of sp– convergent sequence in intuitionistic fuzzy metric spaces and analyze relations of convergence, sp– convergence, s∞– convergence and st– convergence in intuitionistic fuzzy metric spaces. Further, we examine sp– convergence, s∞– convergence and st– convergence using the subsequence of convergent sequence in intuitionistic fuzzy metric spaces. Stationary intuitionistic fuzzy metric spaces are defined and investigated. We Finally define sp– closed sets, s∞– closed sets and st– closed sets in intuitionistic fuzzy metric spaces and investigate relations of them.

scholarly journals On the Lacunary Statistical Convergence of Triple Sequences in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mehmet Gürdal ◽  
Ekrem Savaş
Keyword(s):  
Metric Space ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Research Paper ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Basic Properties ◽  
Fuzzy Metric ◽  
Lacunary Statistical Convergence

Abstract In this research paper, we analyze the lacunary statistical convergence and lacunary statistical Cauchy concepts of triple sequence in fuzzy metric space. We also introduce the concept of triple lacunary statistical completeness and prove some basic properties.

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