Statistically Convergent and Cesáro Summable Fuzzy Real-valued Triple Sequences

Volume 1, Issue 1, October 2016     |     PP. 1-18      |     PDF (839 K)    |     Pub. Date: October 15, 2016
DOI:    452 Downloads     8015 Views  

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 real-valued 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 real-valued Cesáro summable triple sequence space is introduced. A relation between strongly p-Cesáro summability and bounded statistically convergent triple sequences has been established.

Keywords
Fuzzy real-valued 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 Real-valued Triple Sequences , SCIREA Journal of Computer. Volume 1, Issue 1, October 2016 | PP. 1-18.

References

[ 1 ] R. P. Agnew, On summability of multiple sequences, American Journal of Mathematics; 1(4), 62-68, (1934).
[ 2 ] J. S. Connor, The statistical and strong p-Cesáro convergence of sequences, Analysis; 8, 47-63, (1988).
[ 3 ] N. R. Das, A. Choudhury, Boundedness of fuzzy real-valued sequences, Bull. Cal. Math. Soc.; 90, 35-44, (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), 16-22, (2013).
[ 5 ] A.Esi, -Statistical convergence of triple sequences on probabilistic normed space, Global Journal of Mathematical Analysis; 1(2), 29-36, (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), 29-33, (2013).
[ 7 ] H. Fast, Surla convergence statistique, Colloq. Math.; 2, 241-244, (1951).
[ 8 ] J. A. Fridy, On statistical convergence, Analysis; 5, 301-313, (1985).
[ 9 ] J. A. Fridy, C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc.; 125(12), 3625-3631, (1997).
[ 10 ] P. Kumar, V. Kumar, S. S. Bhatia, Multiple sequence of Fuzzy numbers and theirstatistical convergence, Mathematical Sciences, Springer, 6(2), 1-7, (2012).
[ 11 ] J. S. Kwon, On statistical and p-Cesáro convergence of fuzzy numbers, Korean J. Comput. Appl. Math.; 7, 195–203, (2000).
[ 12 ] L.J. Maddox, A tauberian condition for statistical convergence, Math. Proc. Camb. PhilSoc.; 106, 272-280, (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; 33,123-126, (1989).
[ 15 ] M. Nath, S. Roy, On fuzzy real-valued multiple sequence spaces International Journal of Emerging Trends in Electrical and Electronics; 11(4), 103-107, (2015).
[ 16 ] M. Nath, S. Roy, Some new classes of fuzzy real-valued ideal convergent multiple sequence spaces, Asian Journal of Mathematics and Computer Research; 11(4), 272-288, (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), 1579-1584, (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), 49-55, (2007).
[ 20 ] A.Sahiner, B. C. Tripathy, Some I -related Properties of Triple Sequences, Selcuk J. Appl. Math.; 9(2), 9-18, (2008).
[ 21 ] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca; 30, 139-150,(1980).
[ 22 ] E. Savas, On statistically convergent sequences of fuzzy numbers, Inform. Sci.; 137(1-4), 277-282, (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), 226-236, (2012).
[ 24 ] E. Savas, M. Mursaleen, On statistically convergent double sequences of fuzzy numbers, Inform. Sci.; 162(3-4), 183-192, (2004).
[ 25 ] P. V. Subrahmanyam, Cesáro summability of fuzzy real numbers, J. Analysis; 7, 159-168, (1999).
[ 26 ] B. C. Tripathy, Statistically convergent double sequences, Tamkang J. Math.; 34(3), 231-237, (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), 835-848, (2007).
[ 28 ] B. C. Tripathy, A. J. Dutta, Statistically convergence triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis; 4(2), 16-22, (2013).
[ 29 ] B. C. Tripathy, R. Goswami, On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones Journal of Mathematics; 33(2), 157-174, (2014).
[ 30 ] B. C. Tripathy, M. Sen, On generalized statistically convergent sequences, Indian Jour. Pure Appl. Math.; 32(11), 1689-1694, (2001).
[ 31 ] B. K. Tripathy, S. Nanda, Absolute value of fuzzy real numbers and fuzzy sequence spaces, Jour. Fuzzy Math.; 8(4), 883-892, (2000).
[ 32 ] [32] L. A. Zadeh, Fuzzy sets, Information and Control; 8, 338-353, (1965).