Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON LACUNARY STATISTICALLY CONVERGENT DOUBLE SEQUENCES OF FUZZY NUMBERS

  • Published : 2008.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.

Keywords

References

  1. B. Altay and F. Basar, Some new spaces of double sequences, J. Math. Anal. Appl. 309 (2005), no. 1, 70-90 https://doi.org/10.1016/j.jmaa.2004.12.020
  2. R. C. Buck, Generalized asymptotic density, Amer. J. Math. 75 (1953), 335-346 https://doi.org/10.2307/2372456
  3. P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems 35 (1990), 241-249 https://doi.org/10.1016/0165-0114(90)90197-E
  4. H. Fast, Sur la convergence statistique, Colloquium Math. 2 (1951), 241-244
  5. A. R. Freedman, J. J. Sember, and M. Raphael, Some Cesaro-type summability spaces, Proc. London Math. Soc. 37 (1978), no. 3, 508-520 https://doi.org/10.1112/plms/s3-37.3.508
  6. J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), no. 1, 43-51 https://doi.org/10.2140/pjm.1993.160.43
  7. J. A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl. 173 (1993), no. 2, 497-504 https://doi.org/10.1006/jmaa.1993.1082
  8. J. S. Kwon, On statistical and p-Cesaro convergence of fuzzy numbers, Korean J. Comput. Appl. Math. 7 (2000), no. 1, 195-203
  9. M. Matloka, Sequences of fuzzy numbers, BUSEFAL 28 (1986), 28-37
  10. M. Mursaleen and M. Basarir, On some new sequence spaces of fuzzy numbers, Indian J. Pure and Appl. Math. 34 (2003), no. 9, 1351-1357
  11. S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems 33 (1989), 123-126 https://doi.org/10.1016/0165-0114(89)90222-4
  12. F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets and Systems 99 (1998), 353-356 https://doi.org/10.1016/S0165-0114(98)00031-1
  13. F. Nuray and E. Savas, Statistical convergence of fuzzy numbers, Math. Slovaca 45 (1995), no. 3, 269-273
  14. A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), no. 3, 289-321 https://doi.org/10.1007/BF01448977
  15. E. Savas and M. Mursaleen, On statistically convergent double sequences of fuzzy numbers, Inform. Sci. 162 (2004), no. 3-4, 183-192 https://doi.org/10.1016/j.ins.2003.09.005
  16. E. Savas and R. F. Patterson, Lacunary statistical convergence of multiple sequences, Appl. Math. Lett. 20 (2007), no. 9, 964-970 https://doi.org/10.1016/j.aml.2005.06.018
  17. I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375 https://doi.org/10.2307/2308747
  18. B. C. Tripathy, Statistically convergent double sequences, Tamkang J. Math. 34 (2003), no. 3, 231-237
  19. L. A. Zadeh, Fuzzy sets, Inform and Control 8 (1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X

Cited by

  1. Paranormed I-convergent Double Sequence Spaces Associated with Multiplier Sequences vol.54, pp.2, 2014, https://doi.org/10.5666/KMJ.2014.54.2.321