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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.  ...  a b s t r a c t 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  ... 
doi:10.1016/j.mcm.2011.07.020 fatcat:4uftu43cibd4ho2fyuprtbwplm

Lacunary Statistical Convergence of Multiple Sequences in Intuitionistic Fuzzy Normed Spaces

Ekrem Savaş
2014 Mathematical and Computational Applications  
In this paper we introduce the notion ideal statistical convergence and ideal lacunary statistical convergence of multiple sequences with respect to the intuitionistic fuzzy norm   , v  , investigate  ...  In [9] , Mursaleen and Mohiuddine extended the idea of lacunary statistical convergence with respect to the intuitionistic fuzzy normed space.  ...  v SI   It can be checked as in the case of I-double statistically and I-double lacunary statistically convergent sequences with respect to the intuitionistic fuzzy normed space   , v   ... 
doi:10.3390/mca19030241 fatcat:pe4rvx33afhajk2wyvesx6seja

Lacunary Δ-statistical convergence in intuitionistic fuzzy n-normed space

Selma Altundağ, Esra Kamber
2014 Journal of Inequalities and Applications  
In this article, we introduce the notion of lacunary -statistically convergent and lacunary -statistically Cauchy sequences in an intuitionistic fuzzy n-normed space.  ...  The concept of lacunary statistical convergence was introduced in intuitionistic fuzzy n-normed spaces in Sen and Debnath (Math. Comput. Model. 54:2978-2985.  ...  Acknowledgements The authors would like to thank the referees for their careful reading of the manuscript and for their suggestions.  ... 
doi:10.1186/1029-242x-2014-40 fatcat:np5cqsjkcrb53k3curyy5q6yv4

Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces

Pradip Debnath
2012 Computers and Mathematics with Applications  
the notion of lacunary ideal convergence in intuitionistic fuzzy normed linear spaces as a variant of the notion of ideal convergence.  ...  Intuitionistic fuzzy normed linear space Lacunary ideal convergence Lacunary convergence Lacunary I-limit point Lacunary I-cluster point a b s t r a c t The aim of this article is to introduce and study  ...  And thanks to the Editor in Chief for his support and valuable suggestions.  ... 
doi:10.1016/j.camwa.2011.11.034 fatcat:iqn5gl6ydvdlxlqoytd7pt4yza

Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces

Mausumi Sen, Mikail Et
2018 Boletim da Sociedade Paranaense de Matemática  
In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give  ...  The notion of strong Cesaro summability in intuitionistic fuzzy normed linear spaces has been introduced and studied.  ...  The aim of the present paper is to introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear  ... 
doi:10.5269/bspm.v38i1.34814 fatcat:e5a2jlan5jcidnwryx6c6kyt7i

On Ideal Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

Vatan KARAKAYA, Necip ŞİMŞEK, M�zeyyen ERTÜRK, Faik GÜRSOY
2014 Applied Mathematics & Information Sciences  
fuzzy normed spaces, and to investigate relations among concepts such as I−convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed space.  ...  In this work, our purpose is to introduce I−convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I−convergence, the sequences of functions and the intuitionistic  ...  [13] defined statistical convergence in intuitionistic fuzzy normed spaces (IFNS for short) and Mursaleen et al. [22] investigated statistical convergence of double sequences in IFNS.  ... 
doi:10.12785/amis/080525 fatcat:nvhsib7vdnaxjlvetpdphflatq

ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

Ömer Kişi
2021 Facta Universitatis Series Mathematics and Informatics  
In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship,  ...  We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.  ...  Our study of I 2 -statistical convergence and I 2 -lacunary statistical convergence of sequences in IFN spaces also provides a tool to deal with convergence problems of sequences of fuzzy real numbers.  ... 
doi:10.22190/fumi201027032k fatcat:gl5fklwtfrhtfe3cd5q6eaigya

The Rough Intuitionistic Fuzzy Zweier Lacunary Ideal Convergence of Triple Sequence Spaces

Ayhan Esi, Nagarajan Subramanian, Vakeel Ahmad Khan
2018 Journal of Mathematics and Statistics  
In this article, we introduce rough intuitionistic fuzzy Lacunary ideal convergent of triple sequence spaces via zwier operators. We discuss general topological properties.  ...  We introduced and studied the concept of I-convergence of triple sequences in metric spaces where I is an ideal.  ...  Introduction The idea of rough convergence was first introduced by Phu (2001; 2002; 2003) in finite dimensional normed spaces.  ... 
doi:10.3844/jmssp.2018.72.78 fatcat:uyeidnj535d6hakcg2cjf5og4e

Generalized Statistical Convergence in Intuitionistic Fuzzy 2− Normed Space

Ekrem Savas
2015 Applied Mathematics & Information Sciences  
In this paper, we shall introduce the new notion namely, I -λ statistical convergence by using ideal with respect to the intuitionistic fuzzy norm (µ, v) 2 .  ...  We also study the relation between I -λ statistical convergence and I -statistical convergence. subjclass[2000] 40A05; 40B50; 46A19; 46A45.  ...  λ −Statistical convergence in IF2NS In this section we study the concept of I -λ -statistical convergence in the intuitionistic fuzzy 2− normed space (µ, v) 2 .  ... 
doi:10.12785/amis/091l07 fatcat:sip5zlgysjbrlpflsvvseyzt4a

Lacunary Statistical Limit Points in Random 2-Normed Spaces

A. Güncan, U. Yamancı, M. Gürdal
2013 ISRN Mathematical Analysis  
We introduce the notion θ-cluster points, investigate the relation between θ-cluster points and limit points of sequences in the topology induced by random 2-normed spaces, and prove some important results  ...  In [13] , Mursaleen and Mohiuddine extended the idea of lacunary statistical convergence with respect to the intuitionistic fuzzy normed space.  ...  Also lacunary statistically convergent double sequences in probabilistic normed space was studied by Mohiuddine and Savaş in [14] .  ... 
doi:10.1155/2013/189721 fatcat:32djufmokrhjhai5s4rshfiyky

On Lacunary Ideal Convergence in Random -Normed Space

U. Yamancı, M. Gürdal
2013 Journal of Mathematics  
We introduce the notions of lacunary -convergence and lacunary -Cauchy in the topology induced by random -normed spaces and prove some important results.  ...  in intuitionistic fuzzy normed linear spaces.  ...  In [25] , Mursaleen and Mohiuddine extended the idea of lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, and Debnath [26] investigated lacunary ideal convergence  ... 
doi:10.1155/2013/868457 fatcat:kzedhidfabgdjiajhhefq55f2m

Page 2974 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
In addition, the inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers are given.” 04 SET THEORY 99e:04004 04A72 Yao, Y.  ...  Also we introduce the concept of lacunary statistically Cauchy sequence and show that it is equiva- lent to lacunary statistical convergence.  ... 

On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

Awad A. Bakery, Mustafa M. Mohammed
2014 Abstract and Applied Analysis  
Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points.  ...  In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space.  ...  Acknowledgments Many thanks are due to the editor and the anonymous referee for careful reading of the paper and valuable suggestions which helped in improving an earlier version of it.  ... 
doi:10.1155/2014/101782 fatcat:gxynxhwiyfgaflznljdhpeouxe

Rough statistical convergence in intuitionistic fuzzy normed spaces

Reena Antal, Meenakshi Chawla, Vijay Kumar
2021 Filomat  
In this paper, we have defined rough statistical convergence in intuitionistic fuzzy normed spaces which is an useful characterization in the field of statistical convergence.  ...  We have proved some properties related to rough convergence which provides some new functional tools in the situation of uncertainty like intuitionistic fuzzy normed spaces.  ...  Acknowledgement We express great sense of gratitude and deep respect to the referees of this paper and reviewers for their valuable suggestions.  ... 
doi:10.2298/fil2113405a fatcat:rlgdollsevajbkd6rtjzde6z3y

Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces

S. A. Mohiuddine, Bipan Hazarika, Abdullah Alotaibi
2013 Abstract and Applied Analysis  
We define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them.  ...  Further, we introduce the concepts of doubleθ-summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.  ...  [20] and Mursaleen and Mohiuddine [21] defined these notions for double sequences in fuzzy normed spaces and intuitionistic fuzzy normed spaces, respectively. Recently, Mohiuddine et al.  ... 
doi:10.1155/2013/507962 fatcat:ejlt6a2ynnh5ta4nijp5vyzyo4
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