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

Ömer Kişi, Huseyin Isik
2021 Journal of Mathematics  
2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS).  ...  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  ...  Kramosil and Michalek [20] investigated fuzzy metric space (FMS) utilizing the concepts fuzzy and probabilistic metric space. e FMS as a distance between two points to be a nonnegative fuzzy number was  ... 
doi:10.1155/2021/6897038 fatcat:636xisr7mjcvlpm5q6seymw7pu

Statistically Convergent Sequences in Intuitionistic Fuzzy Metric Spaces

Banu Pazar Varol
2022 Axioms  
in fuzzy metric spaces.  ...  In this paper, we introduce the concepts of statistical convergence and statistical Cauchy sequences with respect to the intuitionistic fuzzy metric spaces inspired by the idea of statistical convergence  ...  [22] introduced statistically convergent sequences in fuzzy metric spaces. In view of this, we pay attention to statistical convergence on intuitionistic fuzzy metric spaces with this study.  ... 
doi:10.3390/axioms11040159 fatcat:yhlsyxbfkfdibmyu6ydu4n4aty

Some Summability Spaces of Double Sequences of Fuzzy Numbers

Manmohan Das
2013 IOSR Journal of Mathematics  
  are complete metric spaces.  ...  Let Now one can find that, On Some Summability Spaces of Double Sequences of Fuzzy Numbers This completes the proof.  is a complete metric space under the metric h defined by -Proof: Proof is same with  ...  In [13] Savaş studied the space m(∆), which we call the space of ∆-bounded sequence of fuzzy numbers and showed that this is a complete metric space.  ... 
doi:10.9790/5728-0934549 fatcat:moxpjmzeovexpcjg63rz74222e

On Some Summability Spaces of Sequences of Fuzzy Numbers

Manmohan Das
2013 IOSR Journal of Mathematics  
In this article we introduce and study the notions of ( , ) s vr  ...  It is straightforward to see that d is a metric on L(R). In fact (L(R), d) is a complete metric space. For X, YL(R) define X ≤ Y iff X α ≤ Y α for any α[0, 1].  ...  In [13] Savaş studied the space m(∆), which we call the space of ∆-bounded sequence of fuzzy numbers and showed that this is a complete metric space.  ... 
doi:10.9790/5728-0861216 fatcat:eacd2rahajblvlphfp7j4oth7i

Some Fixed Point Theorems in and966-and968 weak contraction on Fuzzy Metric Space

R. Krishnakumar, Department of Mathematics,Urumu Dhanalakshmi College, Tiruchirappalli, India, Department of Mathematics,Urumu Dhanalakshmi College, Tiruchirappalli, India, Department of Mathematics,Jamal Mohamed College (Autonomous),Tiruchirappalli, India, K. Dinesh, D. Dhamodharan
2018 International Journal of Scientific Research in Mathematical and Statistical Sciences  
In this paper, we discuss some results on fixed point theorems in weak contraction on fuzzy metric spaces, which are study of generalisation of some existing results are also given in the form of corollary  ...  Then is topology on , called the topology induced by the fuzzy metric . . A fuzzy metric space in which every Cauchy sequence is convergent is said to be complete. 4.  ...  A fuzzy metric space in which every sequence has a convergent subsequence is said to be compact Let be a complete strong fuzzy metric space with continuous t-norm and let is a self-mapping in .  ... 
doi:10.26438/ijsrmss/v5i3.146152 fatcat:3e6auzwxcfggzfjnmdfj4fgykq

Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces

Mausumi Sen, Pradip Debnath
2011 Mathematical and computer modelling  
In this article we introduce the notion of lacunary statistically convergent and lacunary statistically Cauchy sequences in intuitionistic fuzzy n-normed linear spaces and give their characterization.  ...  We show that some properties of lacunary statistical convergence of real sequences also hold for sequences in this space.  ...  Later on fuzzy logic became an important area of research in various branches of mathematics such as metric and topological spaces [2-4], theory of functions [5,6], approximation theory [7], etc.  ... 
doi:10.1016/j.mcm.2011.07.020 fatcat:4uftu43cibd4ho2fyuprtbwplm

Constructing of Some New Results in Intuitionistic Fuzzy Metric Space by Applying the Abstraction of Fuzzy Iterated Contraction

2021 Journal of Contemporary Issues in Business and Government  
In this paper, we establish a couple of fixed-point results for fuzzy iterated contraction in the intuitionistic fuzzy metric space. Obtained results are generalization form of well-known results .  ...  The established results can further be generalized for soft sets as fixed point theorems for fuzzy soft sets or soft fuzzy sets.  ...  Kramosil and Michalek [13] generalize the statistical metric space and it is considered a fuzzy metric space.  ... 
doi:10.47750/cibg.2021.27.02.430 fatcat:rbrjzuqh3vholmr5tcebdl4cpu

On λ¯-Statistically Convergent Double Sequences of Fuzzy Numbers

Ekrem Savaş
2008 Journal of Inequalities and Applications  
We study the notion of λ-statistically convergent for double sequence of fuzzy numbers and also get some inclusion relations.  ...  Introduction Nanda 1 studied sequence of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers form a complete metric space.  ...  In 5 , Savaş generalized the statistical convergence by using de la Vallee-Poussin mean.  ... 
doi:10.1155/2008/147827 fatcat:v56rkd7gpzhedao6vlo4qggeei

On statistically convergent double sequences of fuzzy numbers

E Savaş, Mursaleen
2004 Information Sciences  
We study the notion of λ-statistically convergent for double sequence of fuzzy numbers and also get some inclusion relations.  ...  Introduction Nanda 1 studied sequence of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers form a complete metric space.  ...  In 5 , Savaş generalized the statistical convergence by using de la Vallee-Poussin mean.  ... 
doi:10.1016/j.ins.2003.09.005 fatcat:dcrrnvcf5bbifhyocqqzutca3e

On Λ− Summable Of Orlicz Space Of Gai Sequences Of Fuzzy Numbers

N.Subramanian, S.Krishnamoorthy, S. Balasubramanian
2010 Zenodo  
In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.  ...  In recent years, generalizations of statistical convergence have appeared in the study of strong integral summability and the structure of ideals of bounded continuous functions on locally compact spaces  ...  Moreover, statistical convergence is closely related to the concept of convergence in probability. The notion depends on the density of subsets of the subset N of natural numbers.  ... 
doi:10.5281/zenodo.1330666 fatcat:xfe7xyze3nhkzbuooxcxkysl54

On Some Double Lacunary Sequence Spaces of Fuzzy Numbers

Ekrem Savas
2010 Mathematical and Computational Applications  
In this paper we introduce a new concept for lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space of fuzzy numbers.  ...  We also show that if a sequence is lacunary strong Pconvergence with respect to an Orlicz function then it is , ( ) r s S F θ -convergent.  ...  In [18] , Nanda studied on sequences of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers forms a complete metric space.  ... 
doi:10.3390/mca15030439 fatcat:ejqxswst3zgdbfjy5rdjforbvm

On almost λ- statistical convergence of fuzzy numbers - doi: 10.4025/actascitechnol.v36i1.16218

Ayhan Esi, Mehmet Acikgoz
2013 Acta Scientiarum: Technology  
It is also shown that almost λstatistical convergence and strongly almost λ-convergence are equivalent for almost bounded sequences of fuzzy numbers.  ...  The purpose of this paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λconvergence of fuzzy numbers. We obtain some results related to these concepts.  ...  It is well-known that       , n R C is a complete metric space.  ... 
doi:10.4025/16218 fatcat:vyu5pxhasbdrhabvyrxj4izugm

On almost λ- statistical convergence of fuzzy numbers - doi: 10.4025/actascitechnol.v36i1.16218

Ayhan Esi, Mehmet Acikgoz
2013 Acta Scientiarum: Technology  
It is also shown that almost λstatistical convergence and strongly almost λ-convergence are equivalent for almost bounded sequences of fuzzy numbers.  ...  The purpose of this paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λconvergence of fuzzy numbers. We obtain some results related to these concepts.  ...  It is well-known that       , n R C is a complete metric space.  ... 
doi:10.4025/actascitechnol.v36i1.16218 fatcat:wcdpnbhv2bf7tnwefbvp22jqk4

Statistically Convergent Fuzzy Sequence Spaces by Fuzzy Metric

Paritosh Chandra Das
2014 Kyungpook Mathematical Journal  
In this article we study different properties of the statistically convergent and statistically null sequence classes of fuzzy real numbers with fuzzy metric, like completeness, solidness, sequence algebra  ...  A fuzzy real number X is a fuzzy set on R, i.e. a mapping X : R → I(= [0, 1]) associating each real number t with its grade of membership X(t). Definition 2.3.  ...  Though some work have been done on statistically convergent sequences of fuzzy real numbers under classical metric, but a very little work has been done on fuzzy metric.  ... 
doi:10.5666/kmj.2014.54.3.413 fatcat:5ouqkgumkbbevggiw4oyingx3e

Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces

Muhammed Recai Turkmen
2017 Applied and Computational Mathematics  
In this paper, it is introduced the concept of lacunary statistical convergence with respect to a fuzzy norm by using lacunary statistical convergence of a sequence and statistical convergent of a sequence  ...  with respect to fuzzy norm.  ...  Šalát [19] etc studied the concept of statistical convergence in summability theory. in X is statistically convergent to L X ∈ with respect to the fuzzy norm on X provided that for each 0 ε > , we have  ... 
doi:10.11648/j.acm.20170605.13 fatcat:ozcbo7glkzehhbmxpvnzealide
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