Lacunary I-convergent sequences of fuzzy real numbers
DOI:
https://doi.org/10.4067/S0716-09172015000300001Keywords:
Fuzzy real numbers, Lacunary sequence, I-convergence, Symmetric, Convergence free, Sequence algebra.Abstract
In this article we have studied on lacunary I-convergent sequences of fuzzy real numbers. We verify and establish some algebraic properties such as linearity, symmetric, convergence free etc. and also established some other results.References
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[13] B. C. Tripathy, On generalized difference paranormed statistically convergent sequences, Indian J. Pure Appl. Math. 35(5), pp. 655-663, (2004).
[14] B. C. Tripathy, A. Baruah, New type of difference sequence spaces of fuzzy real numbers, Math. Modelling. Anal., 14 (3), pp. 391-397, (2009).
[15] B. C. Tripathy, A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50, pp. 565-574, (2010).
[16] B. C. Tripathy, S. Borgogain, The sequence space m(M,0, Am,p)F , Math. Modelling Anal., 13 (4), pp. 577-586, (2008).
[17] B. C. Tripathy, A. J. Dutta, On fuzzy real-valued double sequence spaces 2c p F , Math. Comput. Modelling, 46 (9-10), pp. 1294-1299, (2007).
[18] B. C. Tripathy, A. J. Dutta, Bounded variation double sequence space of fuzzy real numbers, Comput. Math. Appl., 59 (2), pp. 1031-1037, (2010).
[19] B. C. Tripathy, B. Hazarika, I-convergent sequence spaces associated with multiplier sequence spaces, Math. Ineq. Appl., 11 (3), pp. 543- 548, (2008).
[20] B. C. Tripathy, B. Hazarika, Paranormed I-convergent sequences spaces, Math. Slovaca, 59 (4), pp. 485-494, (2009).
[21] B. C. Tripathy, B. Hazarika, I-convergent sequences spaces defined by Orlicz function, Acta Math. Appl. Sin. (Engl. Ser.), 27 (1), pp. 149-154, (2011).
[22] B. C. Tripathy, S. Mahanta, On I-acceleration convergence of sequences, J. Franklin Inst., 347, pp. 591-598, (2010).
[23] B. C. Tripathy, B. Sarma, Statistically convergent difference double sequence spaces, Acta Math. Sin., 24 (5), pp. 737-742, (2008).
[24] B. C. Tripathy, B. Sarma, Sequence spaces of fuzzy real numbers de- fined by Orlicz functions, Math. Slovaca, 58 (5), pp. 621-628, (2008).
[25] B. C. Tripathy, M. Sen, On generalized statistically convergent sequences, Indian J. Pure Appl. Math., 32 (11), pp. 1689-1694, (2001).
[26] B. C. Tripathy, A. J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers, J. Intelligent Fuzzy Systems, 24, pp. 185-189, (2013).
[2] Y. Altin, M. Et, R. Colak, Lacunary statistical and lacunary strongly convergence of generalized difference sequences of fuzzy numbers, Comput. Math. Appl., 52, pp. 1011-1020, (2006).
[3] Y. Altin, M. Mursaleen, H. Altinok, Statistical summability (C, 1) for sequences of fuzzy real numbers and a Tauberian theorem, J. Intelligent Fuzzy Systems, 21 (6), pp. 379-384, (2010).
[4] T. Bligin, Lacunary strongly A-convergent sequences of fuzzy numbers, Inf. Sci., 160 (1-4), pp. 201-206, (2004).
[5] J. A. Friday, C. Orhan, Lacunary statistical convergence; Pacific J. Math., 160 (1), pp. 43-51, (1993).
[6] A. R. Freedman, J. J. Sember, M. Raphael, Some Cesàro type summability spaces, Proc. London. Math. Soc., 37, pp. 508-520, (1978).
[7] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange, 26 (2), pp. 669-686, (2000-2001).
[8] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets Systems, 99, pp. 353-356, (1998).
[9] T. Salat, B. C. Tripathy, M. Ziman, On some properties of Iconvergence, Tatra Mt. Math. Publ., 28 , pp. 279-286, (2004).
[10] T. Salat, B. C. Tripathy, M. Ziman, On I-convergence field, Italian J. Pure Appl., Math. 17, pp. 45-54, (2005).
[11] E. Savas, New double sequence spaces of fuzzy numbers, Quaestiones Mathematicae, 33, pp. 449-456, (2010).
[12] B. C. Tripathy, Matrix transformation between some classes of sequences, J. Math. Anal. Appl., 206, pp. 448-450, (1997).
[13] B. C. Tripathy, On generalized difference paranormed statistically convergent sequences, Indian J. Pure Appl. Math. 35(5), pp. 655-663, (2004).
[14] B. C. Tripathy, A. Baruah, New type of difference sequence spaces of fuzzy real numbers, Math. Modelling. Anal., 14 (3), pp. 391-397, (2009).
[15] B. C. Tripathy, A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50, pp. 565-574, (2010).
[16] B. C. Tripathy, S. Borgogain, The sequence space m(M,0, Am,p)F , Math. Modelling Anal., 13 (4), pp. 577-586, (2008).
[17] B. C. Tripathy, A. J. Dutta, On fuzzy real-valued double sequence spaces 2c p F , Math. Comput. Modelling, 46 (9-10), pp. 1294-1299, (2007).
[18] B. C. Tripathy, A. J. Dutta, Bounded variation double sequence space of fuzzy real numbers, Comput. Math. Appl., 59 (2), pp. 1031-1037, (2010).
[19] B. C. Tripathy, B. Hazarika, I-convergent sequence spaces associated with multiplier sequence spaces, Math. Ineq. Appl., 11 (3), pp. 543- 548, (2008).
[20] B. C. Tripathy, B. Hazarika, Paranormed I-convergent sequences spaces, Math. Slovaca, 59 (4), pp. 485-494, (2009).
[21] B. C. Tripathy, B. Hazarika, I-convergent sequences spaces defined by Orlicz function, Acta Math. Appl. Sin. (Engl. Ser.), 27 (1), pp. 149-154, (2011).
[22] B. C. Tripathy, S. Mahanta, On I-acceleration convergence of sequences, J. Franklin Inst., 347, pp. 591-598, (2010).
[23] B. C. Tripathy, B. Sarma, Statistically convergent difference double sequence spaces, Acta Math. Sin., 24 (5), pp. 737-742, (2008).
[24] B. C. Tripathy, B. Sarma, Sequence spaces of fuzzy real numbers de- fined by Orlicz functions, Math. Slovaca, 58 (5), pp. 621-628, (2008).
[25] B. C. Tripathy, M. Sen, On generalized statistically convergent sequences, Indian J. Pure Appl. Math., 32 (11), pp. 1689-1694, (2001).
[26] B. C. Tripathy, A. J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers, J. Intelligent Fuzzy Systems, 24, pp. 185-189, (2013).
How to Cite
[1]
B. C. Tripathy and A. J. Dutta, “Lacunary I-convergent sequences of fuzzy real numbers”, Proyecciones (Antofagasta, On line), vol. 34, no. 3, pp. 205-218, 1.
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