Volume 2, Issue 2, April 2016, Page: 15-21
I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers
Sangita Saha, Department of Mathematics, National Institute of Technology Silchar, 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
Received: Aug. 18, 2016;       Accepted: Aug. 29, 2016;       Published: Oct. 11, 2016
DOI: 10.11648/j.ijmfs.20160202.12      View  2727      Downloads  57
Abstract
In this article, the notion of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. We establish the criterion for any arbitrary triple sequence of fuzzy numbers to be I-statistically pre-Cauchy. It is shown that an I-statistically convergent sequence of fuzzy numbers is I-statistically pre-Cauchy. Moreover a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-pre-Cauchy is established.
Keywords
Ideal, Filter, Statistical Convergence, Ideal Convergence, I-Statistical Convergence, Triple Sequence of Fuzzy Numbers, I-statistical Pre-Cauchy, Orlicz Function
To cite this article
Sangita Saha, Bijan Nath, Santanu Roy, I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers, International Journal of Management and Fuzzy Systems. Vol. 2, No. 2, 2016, pp. 15-21. doi: 10.11648/j.ijmfs.20160202.12
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
R. P. Agnew, On summability of multiple sequences, American Journal of Mathematics; 1 (4), 62-68, (1934).
[2]
M. A. Beigi, T. Hajjari, E. G. Khani, A New Index for Fuzzy Distance Measure, Appl. Math. Inf. Sci.; 9 (6), 3017-3025, (2015).
[3]
M. A. Beigi, M. A. Beigi, T. Hajjari, A Theoretical Development on Fuzzy Distance Measure, Journal of Mathematical Extension (JME); 9 (3), 15-38, (2015).
[4]
J. S. Connor, The statistical and strong p-Cesáro convergence of sequences, Analysis; 8, 47-63, (1988).
[5]
J. S. Connor, J. Fridy, J. Kline, Statistically pre-Cauchy sequences, Analysis; 14, 311-317, (1994).
[6]
P. Das, P. Kostyrko, W. Wilczyński and P. Malik, I and I*convergence of double Sequences, Math. Slovaca; 58 (5), 605-620, (2008).
[7]
P. Das, E. Savas, On I-statistically pre-Cauchy Sequences, Taiwanese Journal of Mathematics, 18 (1), 115-126, (2014).
[8]
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).
[9]
A. J. Dutta, B. C. Tripathy, Statistically pre-Cauchy Fuzzy real-valued sequences defined by Orlicz function, Proyecciones Journal of Mathematics; 33 (3), 235-243, (2014).
[10]
H. Dutta, A Characterization of the Class of statistically pre-Cauchy Double Sequences of Fuzzy Numbers, Appl. Math. Inf. Sci.; 7 (4), 1437-1440, (2013).
[11]
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).
[12]
A. Esi, -Statistical convergence of triple sequences on probabilistic normed space, Global Journal of Mathematical Analysis; 1 (2), 29-36, (2013).
[13]
H. Fast, Surla convergence statistique, Colloq. Math.; 2, 241-244, (1951).
[14]
J. A. Fridy, On statistical convergence, Analysis, 5, 301-313, (1985).
[15]
P. Kostyrko, T. Šalát, W. Wilczyński, I-convergence, Real Anal. Exchange; 26, 669–686, (2000- 2001).
[16]
V. A. Khan, Q. M. Danish Lohani, Statistically pre-Cauchy sequences and Orlicz functions, Southeast Asian Bull. Math.; 31, 1107-1112, (2007).
[17]
P. Kumar, V. Kumar, S. S. Bhatia, Multiple sequence of Fuzzy numbers and theirstatistical convergence, Mathematical Sciences, Springer, 6 (2), 1-7, (2012).
[18]
J. S. Kwon, On statistical and p-Cesáro convergence of fuzzy numbers, Korean J. Comput. Appl. Math.; 7, 195–203, (2000).
[19]
I. J. Maddox, A tauberian condition for statistical convergence, Math. Proc. Camb. PhilSoc.; 106, 272-280, (1989).
[20]
M. Matloka, Sequences of fuzzy numbers, BUSEFAL; 28, 28-37, (1986).
[21]
F. Moričz, Statistical convergence of multiple sequences. Arch. Math.; 81, 82–89, (2003).
[22]
S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems; 33, 123-126, (1989).
[23]
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).
[24]
F, Nuray, E. Savas, Statistical convergence of sequences of fuzzy numbers. Math. Slovaca; 45, 269–273, (1995).
[25]
A. Şahiner, M. Gürdal, F. K. Düden, Triple sequences and their statistical convergence, Seluk J. Appl. Math; 8 (2), 49-55, (2007).
[26]
A. Sahiner, B. C. Tripathy, Some I -related Properties of Triple Sequences, Selcuk J. Appl. Math.; 9 (2), 9-18, (2008).
[27]
T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca; 30, 139-150, (1980).
[28]
T. Šalát, B. C. Tripathy, M. Ziman, On some properties of I-convergence, Tatra Mt. Math. Publ.; 28, 279–286, (2004).
[29]
E. Savas, On statistically convergent sequences of fuzzy numbers, Inform. Sci.; 137 (1-4), 277-282, (2001).
[30]
E. Savas, On strongly-summable sequences of fuzzy numbers, Information Sciences, 125, 181-186, (2000).
[31]
E. Savas, P. Das, A generalized statistical convergence via ideals, Applied Mathematics Letters; 24, 826-830, (2011).
[32]
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).
[33]
M Sen, S. Roy, Some I-convergent double classes of sequences of Fuzzy numbers defined by Orlicz functions, Thai Journal of Mathematics; 11 (1), 111–120, (2013),
[34]
B. C. Tripathy, A. J. Dutta, Statistically convergence triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis; 4 (2), 16-22, (2013).
[35]
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).
[36]
B. C. Tripathy, B. Sarma, Statistically convergent double sequence spaces defined by Orlicz function, Soochow Journal of Mathematics, 32 (2), 211-221, (2006).
[37]
B. C. Tripathy, M. Sen, On generalized statistically convergent sequences, Indian Jour. Pure Appl. Math.; 32 (11), 1689-1694, (2001).
[38]
B. K. Tripathy, B. C. Tripathy, On I-convergence of double sequences, Soochow Journal of Mathematics; 31 (4), 549–560, (2005).
[39]
L. A. Zadeh, Fuzzy sets, Information and Control; 8, 338-353, (1965).
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