Abstract
The purpose of the paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λ-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 λ-convergent with respect to a sequence of Orlicz funtions then it is almost λ-statistical convergent.
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Aytar, S., Pehlivan, S.: Statistically monotonic and statistically bounded sequences of fuzzy numbers, Inform. Sci., 176 (2006), 734–744
Başarır, M., Mursaleen, M.: Some sequence spaces of fuzzy numbers generated by infinite matrices, J. FuzzyMath., 11 (2003), 757–764
Connor, J. S.: The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988), 47–63
Diamond, P., Kloeden, P.: Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35 (1990), 241–249
Fast, H.: Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244
Fridy, J. A.: On statistical convergence, Analysis, 5 (1985), 301–313
Kampthan, P. K., Gupta, M.: Sequence Spaces and Series. New York: Marcel Dekker Inc. (1981)
Krasnoselskii, M. A., Rutickii, Y. B.: Convex Functions and Orlicz Spaces. Groningen, Netherlands (1961)
Lakshmikantham, V., Mohapatra, R. N.: Theory of Fuzzy Differential Equations and Inclusions. New York: Taylor and Francis (2003)
Leindler, L.: Über de la Vale Pounsische Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hung., 16 (1965), 375–378
Lindberg, K.: On subspace of Orlicz sequence spaces, Studia Math. 45 (1973), 379–390
Lindenstrauss, J., Tzafriri, L.: On Orlicz sequence spaces, Isr. J.Math., 10 (1971), 379–390
Lorentz, G. G.: A contribution to the theory of divergent sequences, ActaMath., 80 (1948), 167–190
Maddox, I. J.: A new type of convergence, Math. Proc. Camb. Phil. Soc., 83 (1978), 61–64
Maddox, I. J.: Spaces of strongly summable sequences, Quart. J. Math., 18 (1967), 345–355
Matloka, M.: Sequences of fuzzy numbers, BUSEFAL, 28 (1986), 28–37
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
Parashar, S. D., Choudhary, B.: Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25 (1994), 419–428
Salat, T.: On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–150
Schoenberg, I. J.: The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375
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
Tripathy, B.C., Dutta, A. J.: On fuzzy real-valued double sequence space 2l p F , Math. Comput. Modelling, 46(9–10) (2007), 1294–1299
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
Tripathy, B. C.: Matrix transformations between some classes of sequences, J.Math.Anal. Appl., 206 (1997), 448–450
Zadeh, L. A.: Fuzzy sets, Inform. Control, 8 (1965), 338–353
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Başarır, M., Altundağ, S. & Kayıkçı, M. On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions. Rend. Circ. Mat. Palermo 59, 277–287 (2010). https://doi.org/10.1007/s12215-010-0021-3
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DOI: https://doi.org/10.1007/s12215-010-0021-3