θ - limit point, FIθ - cluster point, Fθ - Cauchy sequence and FIθ - Cauchy sequence in fuzzy n-normed space.

">

On Iθ −Convergence and Some Properties in Fuzzy n-Normed Spaces

Muhammed Recai Turkmen *
Faculty of Education, Afyon Kocatepe University, Afyonkarahisar, Turkey.
Periodicity:October - December'2019
DOI : https://doi.org/10.26634/jmat.8.4.17572

Abstract

In this study, firstly lacunary convergence and lacunary ideal convergence is introduced in fuzzy n-normed spaces. Later, the relation between lacunary convergence and lacunary ideal convergence is investigated in fuzzy n-normed spaces. Finally, we have introduced the concept of FIθ - limit point, FIθ - cluster point, Fθ - Cauchy sequence and FIθ - Cauchy sequence in fuzzy n-normed space.

Keywords

Statistical Convergence, Fuzzy n-normed Spaces, Lacunary Convergence, Ideal Convergence.

How to Cite this Article?

Turkmen, M. R. (2019). On Iθ −Convergence and Some Properties in Fuzzy n-Normed Spaces. i-manager's Journal on Mathematics, 8(4), 10-18. https://doi.org/10.26634/jmat.8.4.17572

References

[1]. Bag, T., & Samanta, S. K. (2008). Fixed point theorems in Felbin's type fuzzy normed linear spaces. Journal of Fuzzy Mathematics, 16(1), 243-260.
[2]. Connor, J. (1988). The statistical and strong p-Cesaro convergence of sequences. Analysis, 8(1-2), 47-64.
[3]. Fast, H. (1951). Sur la convergence statistique. In Colloquium mathematicae (Vol. 2, No. 3-4, pp. 241-244).
[4]. Felbin, C. (1992). Finite dimensional fuzzy normed linear space. Fuzzy sets and Systems, 48(2), 239-248. https://doi.org/ 10.1016/0165-0114(92)90338-5
[5]. Fridy, J. A. (1985). On statistical convergence. Analysis, 5(4), 301-314.
[6]. Fridy, J. A., & Orhan, C. (1993). Lacunary statistical summability. Journal of Mathematical Analysis and Applications, 173(2), 497-504. https://doi.org/10.1006/jmaa.1993.1082
[7]. Hazarika, B. (2014). On ideal convergent sequences in fuzzy normed linear spaces. Afrika Matematika, 25(4), 987-999. https://doi.org/10.1007/s13370-013-0168-0
[8]. Hazarika, B., & Kumar, V. (2014). Fuzzy real valued I-convergent double sequences in fuzzy normed spaces. Journal of Intelligent & Fuzzy Systems, 26(5), 2323-2332.
[9]. Katsaras, A. K. (1984). Fuzzy topological vector spaces II. Fuzzy Sets and Systems, 12(2), 143-154.
[10]. Kostyrko, P., Šalát, T., & Wilczyński, W. (2000). I-convergence, Real Anal. Exchange, 26(2), 669-686.
[11]. Kumar, V., & Kumar, K. (2008). On the ideal convergence of sequences of fuzzy numbers. Information Sciences, 178(24), 4670-4678. https://doi.org/10.1016/j.ins.2008.08.013
[12]. Matloka, M. (1986). Sequences of fuzzy numbers. Busefal, 28(1), 28-37.
[13]. Nanda, S. (1989). On sequences of fuzzy numbers. Fuzzy sets and systems, 33(1), 123-126. https://doi.org/10.1016/0165-0114(89)90222-4
[14]. Narayanan, A., & Vijayabalaji, S. (2005). Fuzzy n-normed linear space. International Journal of Mathematics and Mathematical Sciences, 24, 3963-3977. https://doi.org/10.1155/IJMMS.2005.3963
[15]. Nuray, F. (1998). Lacunary statistical convergence of sequences of fuzzy numbers. Fuzzy Sets and Systems, 99(3), 353- 355. https://doi.org/10.1016/S0165-0114(98)00031-1
[16]. Nuray, F., & Ruckle, W. H. (2000). Generalized statistical convergence and convergence free spaces. Journal of Mathematical Analysis and Applications, 245(2), 513-527.
[17]. Pringsheim, A. (1900). On the theory of doubly infinite sequences of numbers. Mathematische Annalen, 53 (3), 289- 321. https://doi.org/10.1007/BF01448977
[18]. Reddy, B. S. (2010). Statistical convergence in n-normed spaces. In International Mathematical Forum (Vol. 24, pp. 1185-1193).
[19]. Reddy, B. S., & Srinivas, M. (2015). Statistical convergence in fuzzy n-normed spaces. International Journal of Pure and Applied Mathematics, 104(1), 29-42.
[20]. Šalát, T. (1980). On statistically convergent sequences of real numbers. Mathematica slovaca, 30(2), 139-150.
[21]. Schoenberg, I. J. (1959). The integrability of certain functions and related summability methods. The American Mathematical Monthly, 66(5), 361-775. https://doi.org/10.1080/00029890.1959.11989303
[22]. Şençı, C., & Pehlı, S. (2008). Statistical convergence in fuzzy normed linear spaces. Fuzzy Sets and Systems, 159(3), 361- 370. https://doi.org/10.1016/j.fss.2007.06.008
[23]. Steinhaus, H. (1951). Sur la convergence ordinaire et la convergence asymptotique. In Colloquium Mathematicum (Vol. 2, No. 1, pp. 73-74).
[24]. Türkmen, M. R. (2017). On lacunary statistical convergence and some properties in fuzzy n-normed spaces. imanager's Journal on Mathematics, 7(3), 1–9. https://doi.org/10.26634/jmat.7.3.14868
[25]. Türkmen, M. R. (2018). Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary I2-Yakınsaklığı ve Bazı Özellikleri Üzerine. Afyon Kocatepe University Journal of Science and Engineering Sciences, 18(3), 868-877.
[26]. Türkmen, M. R., & Çınar, M. (2017). Lacunary statistical convergence in fuzzy normed linear spaces. Applied and Computational Mathematics, 6(5), 233-237. https://doi.org/10.11648/j.acm.20170605.13
[27]. Türkmen, M. R., & Çınar, M. (2018). λ-statistical convergence in fuzzy normed linear spaces. Journal of Intelligent & Fuzzy Systems, 34(6), 4023-4030.
[28]. Türkmen, M. R., & Dündar, E. (2019). On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces. Journal of Intelligent & Fuzzy Systems, 36(2), 1683-1690.
[29]. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.