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

2021
*
Journal of Mathematics
*

2 -Cesàro

doi:10.1155/2021/6897038
fatcat:636xisr7mjcvlpm5q6seymw7pu
*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 ...##
###
Statistically Convergent Sequences in Intuitionistic Fuzzy Metric Spaces

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. ...

##
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Some Summability Spaces of Double Sequences of Fuzzy Numbers

2013
*
IOSR Journal of Mathematics
*

are complete

doi:10.9790/5728-0934549
fatcat:moxpjmzeovexpcjg63rz74222e
*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*. ...##
###
On Some Summability Spaces of Sequences of Fuzzy Numbers

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, YL(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*. ...

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

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*. ...

##
###
Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces

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. ...

##
###
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*. ...

##
###
On λ¯-Statistically Convergent Double Sequences of Fuzzy Numbers

2008
*
Journal of Inequalities and Applications
*

We study the notion of λ-

doi:10.1155/2008/147827
fatcat:v56rkd7gpzhedao6vlo4qggeei
*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. ...##
###
On statistically convergent double sequences of fuzzy numbers

2004
*
Information Sciences
*

We study the notion of λ-

doi:10.1016/j.ins.2003.09.005
fatcat:dcrrnvcf5bbifhyocqqzutca3e
*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. ...##
###
On Λ− Summable Of Orlicz Space Of Gai Sequences Of Fuzzy Numbers

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. ...

##
###
On Some Double Lacunary Sequence Spaces of Fuzzy Numbers

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*. ...

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

2013
*
Acta Scientiarum: Technology
*

It is also shown that almost λ

doi:10.4025/16218
fatcat:vyu5pxhasbdrhabvyrxj4izugm
*statistical**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 λ*convergence*of*fuzzy*numbers. We obtain some results related to these concepts. ... It is well-known that , n R C is a complete*metric**space*. ...##
###
On almost λ- statistical convergence of fuzzy numbers - doi: 10.4025/actascitechnol.v36i1.16218

2013
*
Acta Scientiarum: Technology
*

It is also shown that almost λ

doi:10.4025/actascitechnol.v36i1.16218
fatcat:wcdpnbhv2bf7tnwefbvp22jqk4
*statistical**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 λ*convergence*of*fuzzy*numbers. We obtain some results related to these concepts. ... It is well-known that , n R C is a complete*metric**space*. ...##
###
Statistically Convergent Fuzzy Sequence Spaces by Fuzzy Metric

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*. ...

##
###
Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces

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 ...

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