THERMAL SCIENCE

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Ömer Kişi

THE λ ̅-STATISTICALLY CONVERGENT DOUBLE SEQUENCES IN FUZZY NORMED SPACES

ABSTRACT
We introduce double λ ̅-statistically convergent sequences and double λ ̅- statistically Cauchy sequences in the fuzzy normed spaces. We study [V,λ ̅] and λ ̅-summabilities for double sequences. In addition, we obtain the relation between these concepts and λ ̅-statistically convergence.
KEYWORDS
λ-convergence, double sequence, summabilities
PAPER SUBMITTED: 2018-09-30
PAPER REVISED: 2018-11-04
PAPER ACCEPTED: 2018-11-22
PUBLISHED ONLINE: 2018-12-16
DOI REFERENCE: https://doi.org/10.2298/TSCI180930339K
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THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S153 - S163]
REFERENCES
  1. Fast, H., Sur la convergence statistique, Colloq. Math, 2 (1951), pp. 241-244.
  2. Fridy, J. A., On statistical convergence, Analysis, 5 (1985), pp. 301-313.
  3. Šalát, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), pp. 139-150.
  4. Katsaras, A. K., Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), pp. 143-154.
  5. Alimohammady, M., Roohi, M., Compactness in fuzzy minimal spaces, Chaos, Solitons and Fract., 28 (2006), pp. 906-912.
  6. Felbin, C., Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992), pp. 239-248.
  7. Kaleva, O., Seikkala, S., On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), pp. 215-229.
  8. Das, N.R., Das, P., Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems, 107 (1999), pp. 349-354.
  9. Xiao, J., Zhu, X., On linearly topological structure and property of fuzzy normed linear space, Fuzzy Sets and Systems, 125 (2002), pp. 153-161.
  10. Bag, T., Samanta, S.K., Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), pp. 513-547.
  11. Cheng, S.C., Mordeson, J.M., Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86 (1994), pp. 429-436.
  12. Matloka, M., Sequences of fuzzy numbers, Busefal, 28 (1986), pp. 28-37. 396
  13. Nanda, S., On sequences of fuzzy numbers, Fuzzy Sets Systems, 33 (1989), pp. 123-126.
  14. Mursaleen, M., Edely, O. H. H., Statistical convergence of double sequences. J. Math. Anal. Appl., 288 (2003), pp. 223-231.
  15. Çakan ,C., Altay, B., Statistically boundedness and statistical core of double sequences. J. Math. Anal. Appl., 317 (2006), 2, pp. 690-697.
  16. Altay, B., Başar, F., Some new spaces of double sequences, J Math Anal Appl., 309 (2005), 1, pp. 70-90.
  17. Tripathy, B.C., Statistical convergence of double sequences, Tamkang J. Math., 34 (2003), 3, pp. 231-237.
  18. Nuray, F., Savaş, E., Statistical convergence of sequences of fuzzy numbers, Math. Slovaca, 45 (1995), 3, pp. 269-273.
  19. Savaş, E., Mursaleen, M., On statistically convergent double sequences of fuzzy numbers, Inform Sci., 162 (2004), pp. 183-192.
  20. Şençimen, C., Pehlivan, S., Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems, 159 (2008), pp. 361-370.
  21. Mohiuddine, et al., Statistical convergence of double sequences in fuzzy normed spaces, Filomat, 26 (2012), 4, pp. 673-681.
  22. Mursaleen, M., λ-statistical convergence, Math. Slovaca, 50 (2000), 1, pp. 111-115.
  23. Savaş, E., On strongly λ-summable sequences of fuzzy numbers. Inform. Sci., 125 (2000), 14, pp. 181-186.
  24. Savaş, E., On -statistically convergent double sequences of fuzzy numbers, Journal of Inequalities and Applications, (2008), Art. ID 147827, pp. 6.
  25. Savaş, E., Patterson, R. F., On double statistical P-convergence of fuzzy numbers, Journal of Inequalities and Applications, (2009), Art. ID 423792, pp . 7
  26. Savaş, E., Patterson, R. F.,  , -double sequence spaces via Orlicz function, J.Comput. Anal. Appl. 10 (2008), 1, pp. 101-111.
  27. Türkmen, M.R., Çınar, M., λ-statistical convergence in fuzzy normed linear spaces, Journal of Intelligent and Fuzzy Systems, 34 (2018), 6, pp. 4023-4030.
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The λ ̅-statistically convergent double sequences in fuzzy normed spaces

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