Statistically Convergent and Cesáro Summable Fuzzy Realvalued Triple Sequences
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Author(s)
Munmun Nath, Department of Mathematics, S.S. College, Hailakandi; Assam, India
Bijan Nath, Department of Mathematics, National Institute of Technology, Silchar; Assam, India
Santanu Roy, Department of Mathematics, National Institute of Technology, Silchar; Assam, India
Abstract
In this article, the notion of different types of statistically convergent and statistically null fuzzy realvalued sequences having multiplicity greater than two is introduced. Some algebraic and topological properties such as solid, monotone, symmetric, convergence free, sequence algebra etc. of these spaces are studied. Also fuzzy realvalued Cesáro summable triple sequence space is introduced. A relation between strongly pCesáro summability and bounded statistically convergent triple sequences has been established.
Keywords
Fuzzy realvalued triple sequence, solid space, symmetric space, convergence free, sequence algebra, density, statistical convergence, statistical Cauchy, Cesáro summable, strong Cesáro summability.
Cite this paper
Munmun Nath,
Bijan Nath,
Santanu Roy,
Statistically Convergent and Cesáro Summable Fuzzy Realvalued Triple Sequences, SCIREA Journal of Mathematics. Vol.
1
, No.
1
,
2016
, pp.
24

43
.
References
[ 1 ]  R. P. Agnew, On summability of multiple sequences, American Journal of Mathematics; 1(4), 6268, (1934). 
[ 2 ]  J. S. Connor, The statistical and strong pCesáro convergence of sequences, Analysis; 8, 4763, (1988). 
[ 3 ]  N. R. Das, A. Choudhury, Boundedness of fuzzy realvalued sequences, Bull. Cal. Math. Soc.; 90, 3544, (1998). 
[ 4 ]  A. J. Dutta, A. Esi, B. C. Tripathy, Statistically convergence triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis; 4(2), 1622, (2013). 
[ 5 ]  A. Esi, Statistical convergence of triple sequences on probabilistic normed space, Global Journal of Mathematical Analysis; 1(2), 2936, (2013). 
[ 6 ]  A. Esi, Statistical convergence of triple sequences in topological groups, Annals of the University of Craiova, Mathematics and Computer Science Series; 40(1), 2933, (2013). 
[ 7 ]  H. Fast, Surla convergence statistique, Colloq. Math.; 2, 241244, (1951). 
[ 8 ]  J. A. Fridy, On statistical convergence, Analysis; 5, 301313, (1985). 
[ 9 ]  J. A. Fridy, C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc.; 125(12), 36253631, (1997). 
[ 10 ]  P. Kumar, V. Kumar, S. S. Bhatia, Multiple sequence of Fuzzy numbers and theirstatistical convergence, Mathematical Sciences, Springer, 6(2), 17, (2012). 
[ 11 ]  J. S. Kwon, On statistical and pCesáro convergence of fuzzy numbers, Korean J. Comput. Appl. Math.; 7, 195–203, (2000). 
[ 12 ]  I. J. Maddox, A tauberian condition for statistical convergence, Math. Proc. Camb. PhilSoc.; 106, 272280, (1989). 
[ 13 ]  F. Moričz, Statistical convergence of multiple sequences. Arch. Math.; 81, 82–89, (2003). 
[ 14 ]  S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems; 33,123126, (1989). 
[ 15 ]  M. Nath, S. Roy, On fuzzy realvalued multiple sequence spaces International Journal of Emerging Trends in Electrical and Electronics; 11(4), 103107, (2015). 
[ 16 ]  M. Nath, S. Roy, Some new classes of fuzzy realvalued ideal convergent multiple sequence spaces, Asian Journal of Mathematics and Computer Research; 11(4), 272288, (2016). 
[ 17 ]  M. Nath, S. Roy, Some new classes of ideal convergent difference multiple sequences of fuzzy real numbers, Journal of Intelligent and Fuzzy systems; 31(3), 15791584, (2016). 
[ 18 ]  F, Nuray, E. Savas, Statistical convergence of sequences of fuzzy numbers. Math. Slovaca; 45, 269–273, (1995). 
[ 19 ]  A. Şahiner, M. Gürdal, F. K. Düden, Triple sequences and their statistical convergence,Seluk J.Appl. Math; 8(2), 4955, (2007). 
[ 20 ]  A. Sahiner, B. C. Tripathy, Some I related Properties of Triple Sequences, Selcuk J. Appl.Math.; 9(2), 918, (2008). 
[ 21 ]  T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca; 30, 139150,(1980). 
[ 22 ]  E. Savas, On statistically convergent sequences of fuzzy numbers, Inform. Sci.; 137(14), 277282, (2001). 
[ 23 ]  E. Savas, A. Esi, Statistical convergence of triple sequences on probabilistic normed Space, Annals of the University of Craiova, Mathematics and Computer Science Series; 39(2), 226236, (2012). 
[ 24 ]  E. Savas, M. Mursaleen, On statistically convergent double sequences of fuzzy numbers, Inform. Sci.; 162(34), 183192, (2004). 
[ 25 ]  P. V. Subrahmanyam, Cesáro summability of fuzzy real numbers, J. Analysis; 7, 159168, (1999). 
[ 26 ]  B. C. Tripathy, Statistically convergent double sequences, Tamkang J. Math.; 34(3), 231237, (2003). 
[ 27 ]  B. C. Tripathy, A. J. Dutta, Statistically convergence and Cesáro summable double sequences of fuzzy real numbers, Soochow journal of Mathematics; 33(4), 835848, (2007). 
[ 28 ]  B. C. Tripathy, A. J. Dutta, Statistically convergence triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis; 4(2), 1622, (2013). 
[ 29 ]  B. C. Tripathy, R. Goswami, On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones Journal of Mathematics; 33(2), 157174, (2014). 
[ 30 ]  B. C. Tripathy, M. Sen, On generalized statistically convergent sequences, Indian Jour. Pure Appl. Math.; 32(11), 16891694, (2001). 
[ 31 ]  B. K. Tripathy, S. Nanda, Absolute value of fuzzy real numbers and fuzzy sequence spaces,Jour. Fuzzy Math.; 8(4), 883892, (2000). 
[ 32 ]  L. A. Zadeh, Fuzzy sets, Information and Control; 8, 338353, (1965). 