On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions. (English) Zbl 1208.46002
Summary: The purpose of the paper is to introduce the concepts of almost \(\lambda\)-statistical convergence and strongly almost \(\lambda\)-convergence of sequences of fuzzy numbers. We establish some connections between these concepts. It is also shown that, if a sequence of fuzzy numbers is strongly almost \(\lambda\)-convergent with respect to a sequence of Orlicz functions, then it is almost \(\lambda\)-statistical convergent.
MSC:
| 46A45 | Sequence spaces (including Köthe sequence spaces) |
| 40A35 | Ideal and statistical convergence |
| 26E50 | Fuzzy real analysis |
References:
| [1] | Aytar, S., Pehlivan, S.: Statistically monotonic and statistically bounded sequences of fuzzy numbers, Inform. Sci., 176 (2006), 734–744 · Zbl 1089.40001 · doi:10.1016/j.ins.2005.03.015 |
| [2] | Başarır, M., Mursaleen, M.: Some sequence spaces of fuzzy numbers generated by infinite matrices, J. FuzzyMath., 11 (2003), 757–764 · Zbl 1047.46053 |
| [3] | Connor, J. S.: The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988), 47–63 · Zbl 0653.40001 |
| [4] | Diamond, P., Kloeden, P.: Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35 (1990), 241–249 · Zbl 0704.54006 · doi:10.1016/0165-0114(90)90197-E |
| [5] | Fast, H.: Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244 · Zbl 0044.33605 |
| [6] | Fridy, J. A.: On statistical convergence, Analysis, 5 (1985), 301–313 · Zbl 0588.40001 |
| [7] | Kampthan, P. K., Gupta, M.: Sequence Spaces and Series. New York: Marcel Dekker Inc. (1981) |
| [8] | Krasnoselskii, M. A., Rutickii, Y. B.: Convex Functions and Orlicz Spaces. Groningen, Netherlands (1961) |
| [9] | Lakshmikantham, V., Mohapatra, R. N.: Theory of Fuzzy Differential Equations and Inclusions. New York: Taylor and Francis (2003) · Zbl 1072.34001 |
| [10] | Leindler, L.: Über de la Vale Pounsische Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hung., 16 (1965), 375–378 · Zbl 0138.28802 · doi:10.1007/BF01904844 |
| [11] | Lindberg, K.: On subspace of Orlicz sequence spaces, Studia Math. 45 (1973), 379–390 · Zbl 0217.16602 |
| [12] | Lindenstrauss, J., Tzafriri, L.: On Orlicz sequence spaces, Isr. J.Math., 10 (1971), 379–390 · Zbl 0227.46042 · doi:10.1007/BF02771656 |
| [13] | Lorentz, G. G.: A contribution to the theory of divergent sequences, ActaMath., 80 (1948), 167–190 · Zbl 0031.29501 |
| [14] | Maddox, I. J.: A new type of convergence, Math. Proc. Camb. Phil. Soc., 83 (1978), 61–64 · Zbl 0392.40001 · doi:10.1017/S0305004100054281 |
| [15] | Maddox, I. J.: Spaces of strongly summable sequences, Quart. J. Math., 18 (1967), 345–355 · Zbl 0156.06602 · doi:10.1093/qmath/18.1.345 |
| [16] | Matloka, M.: Sequences of fuzzy numbers, BUSEFAL, 28 (1986), 28–37 · Zbl 0626.26010 |
| [17] | Mursaleen, M., Khan, Q. A., Chishti, T. A.: Some new convergent sequence spaces defined by Orlicz functions and statistical convergence, Ital. J. Pure Appl. Math., 9 (2001), 25–32 · Zbl 1008.40002 |
| [18] | Parashar, S. D., Choudhary, B.: Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25 (1994), 419–428 · Zbl 0802.46020 |
| [19] | Salat, T.: On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–150 · Zbl 0437.40003 |
| [20] | Schoenberg, I. J.: The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375 · Zbl 0089.04002 · doi:10.2307/2308747 |
| [21] | Talo, Ö., Başar, F.: On the space bv p(F) of sequences of p-bounded variation of fuzzy numbers, Acta Math. Sin. Eng. Ser., 24 (2008), in press · Zbl 1162.46041 |
| [22] | Tripathy, B.C., Dutta, A. J.: On fuzzy real-valued double sequence space 2 l F p , Math. Comput. Modelling, 46(9–10) (2007), 1294–1299 · Zbl 1138.46048 · doi:10.1016/j.mcm.2007.01.006 |
| [23] | Tripathy, B.C., Mahanta, S.: On a class of sequences related to the l p spaces defined by Orlicz function, Soochow J. Math., 29 (2003), 379–391 · Zbl 1046.46007 |
| [24] | Tripathy, B. C.: Matrix transformations between some classes of sequences, J.Math.Anal. Appl., 206 (1997), 448–450 · Zbl 0907.47021 · doi:10.1006/jmaa.1997.5236 |
| [25] | Zadeh, L. A.: Fuzzy sets, Inform. Control, 8 (1965), 338–353 · Zbl 0139.24606 |
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