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On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces

Muhammed Recai Turkmen *

Assistant Professor, Department of Mathematics and Science Education, The Afyon Kocatepe University, Turkey.

Periodicity:July - September'2018
DOI : https://doi.org/10.26634/jmat.7.3.14868

Abstract

In this paper, the author has introduced the concept of lacunary summable and lacunary statistical convergence in fuzzy n-normed spaces. At the same time, the author has introduced condition of being lacunary statistically Cauchy sequence with respect to a fuzzy n-norm. The author has also studied the relation between these concepts and gave some properties of lacunary statistical convergence sequences in fuzzy n-normed spaces.

Keywords

Statistical Convergence, Lacunary Sequence, Fuzzy Normed Space, N-norm.

How to Cite this Article?

Türkmen, M. R. (2018). On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces, i-manager's Journal on Mathematics, 7(3), 1-9. https://doi.org/10.26634/jmat.7.3.14868

References

[1]. Altınok, H., Altın, Y., & Et, M. (2004). Lacunary almost statistical convergence of fuzzy numbers. Thai Journal of Mathematics, 2(2), 265-274.

[2]. Bag, T., & Samanta, S. K. (2008). Fixed point theorems in Felbin's type fuzzy normed linear spaces. Journal of Fuzzy Mathematics, 16(1), 243.

[3]. Diamond, P., & Kloeden, P. E. (1994). Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific.

[4]. Dündar, E., Ulusu. U., & Pancaroğlu, N. (2016). Strongly J₂ -Lacunary Convergence and J₂ -Lacunary Cauchy Double Sequences of Sets. The Aligarh Bulletin of Mathematics, 35 (1-2), 1-15.

[5]. Fast, H. (1951). Sur la convergence statistique. In Colloquium Mathematicae, 2(3-4), 241-244.

[6]. Felbin, C. (1992). Finite dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48(2), 239-248.

[7]. Fridy, J. A. (1985). On statistical convergence. Analysis, 5(4), 301-314.

[8]. Fridy, J. A., & Orhan, C. (1993). Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43-51.

[9]. Matloka, M. (1986). Sequences of fuzzy numbers. Busefal, 28(1), 28-37.

[10]. Misiak, A. (1989). n-inner product spaces. Mathematische Nachrichten, 140(1), 299-319.

[11]. Mizumoto M., & Tanaka, K. (1979). Some properties of fuzzy numbers, North-Holland (Amsterdam): Advances in Fuzzy Set Theory and Applications.

[12]. Nanda, S. (1989). On sequences of fuzzy numbers. Fuzzy Sets and Systems, 33(1), 123-126.

[13]. Narayanan, A., & Vijayabalaji, S. (2005). Fuzzy n-normed linear space. International Journal of Mathematics and Mathematical Sciences, 2005(24), 3963-3977.

[14]. Nuray, F. (1998). Lacunary statistical convergence of sequences of fuzzy numbers. Fuzzy Sets and Systems, 99(3), 353- 355.

[15]. Nuray, F., & Savaş, E. (1995). Statistical convergence of sequences of fuzzy numbers. Mathematica Slovaca, 45(3), 269-273.

[16]. Nuray, F., Ulusu, U., & Dündar, E. (2016). Lacunary statistical convergence of double sequences of sets. Soft Computing, 20(7), 2883-2888.

[17]. Pringsheim, A. (1900). Zur theorie der zweifach unendlichen Zahlenfolgen. Mathematische Annalen, 53(3), 289-321.

[18]. Rath, D., & Tripathy, B. C. (1994). On statistically convergent and statistically Cauchy sequences. Indian Journal of Pure and Applied Mathematics, 25, 381-386.

[19]. Reddy, B. S. & Srinivas, M. (2015). Statistically convergent in fuzzy n-normed spaces. Int. J. of Pure and App. Math., 104 , 29-42.

[20]. Šalát, T. (1980). On statistically convergent sequences of real numbers. Mathematica Slovaca, 30(2), 139-150.

[21]. Savaş, E. (2001). On statistically convergent sequences of fuzzy numbers. Information Sciences, 137(1-4), 277-282.

[22]. Schoenberg, I. J. (1959). The integrability of certain functions and related summability methods. The American Mathematical Monthly, 66(5), 361-375.

[23]. Steinhaus, H. (1951). Sur la convergence ordinaire et la convergence asymptotique. In Colloq. Math, 2(1), 73-74.

[24]. Sencimen, C., & Pehlivan, S. (2008). Statistical convergence in fuzzy normed linear spaces. Fuzzy Sets and Systems, 159(3), 361-370.

[25]. Turkmen, M. R., & Dündar, E. (2018). On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces. Journal of Intelligent & Fuzzy Systems (Preprint), pp.1-8. DOI: 10.3233/JIFS-18841

[26]. Turkmen, M. R., & Cinar, M. (2018). Lambda Statistical Convergence in Fuzzy Normed Linear Spaces. Journal of Intelligent and Fuzzy Systems, 34 (6), 4023-4030.

[27]. Turkmen, M. R., & Cinar, M. (2017). Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces. Applied and Computational Mathematics, 6(5), 233-237.

[28]. Turkmen, M. R., & Efe, H. (2013). On some properties of closability of farthest point maps in fuzzy N-normed spaces. i-manager's Journal on Mathematics, 2(4), 33-38.

[29]. Zadeh, L. A. (1965). Fuzzy sets. Inform. Contr., 8(3) , 338-353.

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