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.

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.

scholarly journals Some new fixed point theorems in generalized intuitionistic fuzzy metric spaces

2019 ◽  
Vol 25 (3) ◽  
pp. 42-52
Author(s):  
M. Rajeswari ◽  
◽  
M. Jeyaraman ◽  
S. Durga ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy

(φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces

2014 ◽  
Vol 26 (5) ◽  
pp. 2497-2504 ◽  
Author(s):  
Ismat Beg ◽  
Calogero Vetro ◽  
Dhananjay Gopal ◽  
Mohammad Imdad
Keyword(s):  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy

scholarly journals Some Results on Wijsman Ideal Convergence in Intuitionistic Fuzzy Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Ayhan Esi ◽  
Vakeel A. Khan ◽  
Mobeen Ahmad ◽  
Masood Alam
Keyword(s):  
Metric Space ◽  
Cauchy Sequence ◽  
Metric Spaces ◽  
General Setting ◽  
Fuzzy Metric Space ◽  
Ideal Convergence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Closed Sets ◽  
Intuitionistic Fuzzy

In the present work, we study and extend the notion of Wijsman J –convergence and Wijsman J ∗ –convergence for the sequence of closed sets in a more general setting, i.e., in the intuitionistic fuzzy metric spaces (briefly, IFMS). Furthermore, we also examine the concept of Wijsman J ∗ –Cauchy and J –Cauchy sequence in the intuitionistic fuzzy metric space and observe some properties.

scholarly journals Some new fixed point results on intuitionistic fuzzy metric spaces

2016 ◽  
Vol 3 (1) ◽  
pp. 1142839 ◽  
Author(s):  
Vishal Gupta ◽  
Ashima Kanwar ◽  
Hari M. Srivastava
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy
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