THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

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
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
CITATION EXPORT: view in browser or download as text file
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.

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence