Some New Classes of Statistical Convergent Fuzzy Real-valued Triple Sequences
Keywords:
Density, triple sequence, statistical convergence, statistically Cauchy, fuzzy real-valued triple sequences, Cesáro summable, strong Cesáro summabilityAbstract
In this article, some new classes of statistical convergence of sequences of fuzzy real numbers have multiplicity greater than two is introduced. Certain Theorems regarding uniqueness of limit, algebraic characterization of statistical limit for triple sequences of fuzzy numbers are obtained. The decomposition theorem is proved. The inclusion relations are derived. The fuzzy real-valued Cesáro summable triple sequence space is also introduced. A relation between strongly p-Cesáro summability and bounded statistically convergent triple sequences has been established.
References
R. P. Agnew, On summability of multiple sequences, American Journal of Mathematics; 1(4), 62-68, (1934).
Y. Altin, A note on lacunary statistically convergent double sequences of fuzzy numbers,Commun. Korean Math. Soc.; 23(2), 179–185, (2008).
J. S. Connor, The statistical and strong p-Cesáro convergence of sequences; Analysis; 8, 47-63, (1988).
K. Demirci, On lacunary statistical limit points, DemonstratoMathematica; 35(1), 93-101, (2002).
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).
A. Esi, 3 -Statistical convergence of triple sequences on probabilistic normed space, Global Journal of Mathematical Analysis; 1(2), 29-36, (2013).
A. Esi, Statistical convergence of triple sequences in topological groups, Annals of theUniversity of Craiova, Mathematics and Computer Science Series; 40(1), 29-33, (2013).
A. Esi, M. K. Ozdemir, Generalized m-statistical convergence in probabilistic normed space, J. Comput. Anal. Appl.; 13(5), 923-932, (2011).
H. Fast, Surla convergence statistique, Colloq. Math.; 2, 241-244, (1951).
J. A. Fridy, On statistical convergence, Analysis; 5, 301-313, (1985).
J. A. Fridy, C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc.; 125(12), 3625-3631, (1997).
. A. Gokhan, M. Et, M. Mursaleen, Almost lacunary statistical and strongly almostlacunary Convergenceof sequences of fuzzy numbers, Math. Comput. Modelling, 49(3-4), 548–555, (2009).
. Kumar, V. Kumar, S. S. Bhatia, Multiple sequence of Fuzzy numbers and their statistical convergence, Mathematical Sciences, Springer; 6(2), 1-7, (2012).
J. S. Kwon, On statistical and p-Cesáro convergence of fuzzy numbers, Korean J. Comput. Appl. Math.; 7, 195–203, (2000).
I. J. Maddox, A tauberian condition for statistical convergence, Math. Proc. Camb. PhilSoc.; 106, 272-280, (1989).
F. Moričz, Statistical convergence of multiple sequences, Arch. Math.; 81, 82–89, (2003).
M. Nath, S. Roy, On fuzzy real-valued multiple sequence spaces 3lF ( p), International Journal of Emerging Trends in Electrical and Electronics; 11(4), 103-107, (2015).
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).
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).
F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets Systems; 99, 353-356, (1998).
F, Nuray, E. Savas, Statistical convergence of sequences of fuzzy numbers. Math. Slovaca; 45, 269–273, (1995).
A. Şahiner, M. Gürdal, F. K. Düden, Triple sequences and their statistical convergence, Seluk J. Appl. Math.; 8(2), 49-55, (2007).
A. Sahiner, B. C. Tripathy, Some I -related Properties of Triple Sequences, Selcuk J. Appl. Math.; 9(2), 9-18, (2008).
T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca; 30, 139-150, (1980).
E.Savas, On statistically convergent sequences of fuzzy numbers. Inform. Sci.; 137(1-4), 277-282, (2001).
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).
E. Savas, M. Mursaleen, On statistically convergent double sequences of fuzzy numbers, Inform. Sci.; 162(3-4), 183-192, (2004).
P. V. Subrahmanyam, Cesáro summability of fuzzy real numbers, J. Analysis; 7, 159-168, (1999).
B. C. Tripathy, Statistically convergent double sequences, Tamkang J. Math.; 34(3), 231-237, (2003).
B. C. Tripathy, A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50, 565-574. (2010).
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).
B. C. Tripathy, A. J. Dutta, Statistically convergence triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis; 4(2), 16-22, (2013).
B.C. Tripathy, B. Sarma, Statistically convergent difference double sequence spaces, Acta Math. Sinica(Eng. Ser.); 24(5), 737-742, (2008).
B. C. Tripathy, M. Sen, On generalized statistically convergent sequences, Indian Jour. Pure Appl. Math.; 32(11), 1689-1694, (2001).
L. A. Zadeh, Fuzzy sets, Information and Control; 8, 338-353, (1965).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 COMPUSOFT: An International Journal of Advanced Computer Technology
This work is licensed under a Creative Commons Attribution 4.0 International License.
©2023. COMPUSOFT: AN INTERNATIONAL OF ADVANCED COMPUTER TECHNOLOGY by COMPUSOFT PUBLICATION is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at COMPUSOFT: AN INTERNATIONAL OF ADVANCED COMPUTER TECHNOLOGY. Permissions beyond the scope of this license may be available at Creative Commons Attribution 4.0 International Public License.
