Applied and Computational Mathematics

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Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces

Received: Jul. 19, 2017    Accepted: Aug. 17, 2017    Published: Oct. 23, 2017
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Abstract

In this paper, it is introduced the concept of lacunary statistical convergence with respect to a fuzzy norm by using lacunary statistical convergence of a sequence and statistical convergent of a sequence with respect to fuzzy norm. It also has studied the relation between these concepts.

DOI 10.11648/j.acm.20170605.13
Published in Applied and Computational Mathematics ( Volume 6, Issue 5, October 2017 )
Page(s) 233-237
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Lacunary Statistical Convergence, Fuzzy Normed Linear Space, Sequences Space

References
[1] H. Altınok, Y. Altın, and M. Et, Lacunary almost statistical convergence of fuzzy numbers, Thai Journal of Mathematics, vol. 2, no. 2, pp. 265–274, 2004.
[2] T. Bag and SK. Samanta, Fixed point theorems in Felbin’s type fuzzy normed linear spaces, J. Fuzzy Math., vol. 16, no. 1, (2008), pp. 243-260.
[3] M. Et; M. Çınar and M. Karakaş, On λ-statistical convergence of order α of sequences of function, J. Inequal. Appl. 2013, 2013:204, pp. 1-8.
[4] R. Çolak, On λ- statistical convergence, Conference on Summability and Applications, May 12-13, 2011, Istanbul Turkey.
[5] J. S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8 (1988), pp. 47-63.
[6] P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets-Theory and Applications. World Scientific Publishing, Singapore, 1994.
[7] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
[8] C. Felbin, Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems 48(2) (1992), 239–248.
[9] J. Fridy, On statistical convergence, Analysis 5 (1985), 301-313.
[10] J. A. Fridy and C. Orhan, Lacunary Statistical Convergence, Pasific Journal of Mathematics, vol. 160, no. 1, 43-51, 1993.
[11] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12(3) (1984), 215–229.
[12] M. Mizumoto and K. Tanaka, Some properties of fuzzy numbers, Advances in Fuzzy Set Theory and Applications, pp. 153–164, North-Holland, Amsterdam, 1979.
[13] F. Nuray, Lacunary Statistical Convergence of Sequence of Fuzzy Numbers, Fuzzy Sets and Systems, 99 (1998) 353,355.
[14] E. Savas, On Strongly λ- summable Sequences of Fuzzy Numbers, Information Science, (125) (1-2), (2000).
[15] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375.
[16] A. R. Freedman, J. J. Sember and M. Raphael, Some Cesaro type summability spaces, Proc. London Math. Soc., 37 (1978), 508-520.
[17] C. Sencimen and S. Pehlivan, Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems 159(3) (2008), 361–370.
[18] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74.
[19] T. Šalát (1980) On statistically convergent sequences of real numbers, Math. Slovaca 30, 139-150.
[20] J. Xiao and X. Zhu, On linearly topological structure and property of fuzzy normed linear space. Fuzzy Sets and Systems 125(2) (2002), 153–161.
[21] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
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  • APA Style

    Muhammed Recai Turkmen, Muhammed Cinar. (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

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    ACS Style

    Muhammed Recai Turkmen; Muhammed Cinar. Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces. Appl. Comput. Math. 2017, 6(5), 233-237. doi: 10.11648/j.acm.20170605.13

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    AMA Style

    Muhammed Recai Turkmen, Muhammed Cinar. Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces. Appl Comput Math. 2017;6(5):233-237. doi: 10.11648/j.acm.20170605.13

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  • @article{10.11648/j.acm.20170605.13,
      author = {Muhammed Recai Turkmen and Muhammed Cinar},
      title = {Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces},
      journal = {Applied and Computational Mathematics},
      volume = {6},
      number = {5},
      pages = {233-237},
      doi = {10.11648/j.acm.20170605.13},
      url = {https://doi.org/10.11648/j.acm.20170605.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20170605.13},
      abstract = {In this paper, it is introduced the concept of lacunary statistical convergence with respect to a fuzzy norm by using lacunary statistical convergence of a sequence and statistical convergent of a sequence with respect to fuzzy norm. It also has studied the relation between these concepts.},
     year = {2017}
    }
    

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Author Information
  • Department of Mathematics, Afyon Kocatepe University, Afyon, Turkey

  • Department of Mathematics, Mus Alparslan University, Mus, Turkey

  • Section