Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME RESULTS ON CONVERGENCES IN FUZZY METRIC SPACES AND FUZZY NORMED SPACES

  • Cho, Kyugeun (Bangmok College of General Education Myong Ji University) ;
  • Lee, Chongsung (Department of Mathematics education Inha University)
  • Received : 2018.11.09
  • Accepted : 2019.06.11
  • Published : 2020.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce the definitions of sp-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, sp-convergence, s∞-convergence and st-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study sp-convergence, s∞-convergence and st-convergence using the sub-sequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define sp-closed sets, s∞-closed sets and st-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.

Keywords

References

  1. T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), no. 3, 687-705.
  2. T. Bag and S. K. Samanta, Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces, Fuzzy Sets and Systems 159 (2008), no. 6, 685-707. https://doi.org/10.1016/j.fss.2007.09.006
  3. K. Cho and C. Lee, On convergneces in fuzzy normed spaces (preprint).
  4. Z. Deng, Fuzzy pseudometric spaces, J. Math. Anal. Appl. 86 (1982), no. 1, 74-95. https://doi.org/10.1016/0022-247X(82)90255-4
  5. C. Felbin, Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems 48 (1992), no. 2, 239-248. https://doi.org/10.1016/0165-0114(92)90338-5
  6. A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), no. 3, 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  7. M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), no. 3, 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
  8. V. Gregori, J. J. Mi-nana, and S. Morillas, A note on convergence in fuzzy metric spaces, Iran. J. Fuzzy Syst. 11 (2014), no. 4, 75-85, 102.
  9. V. Gregori and J.-J. Minana, Strong convergence in fuzzy metric spaces, Filomat 31 (2017), no. 6, 1619-1625. https://doi.org/10.2298/FIL1706619G
  10. V. Gregori and S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems 144 (2004), no. 3, 411-420. https://doi.org/10.1016/S0165-0114(03)00161-1
  11. O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), no. 3, 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  12. R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput. 17 (2005), no. 1-2, 475-484. https://doi.org/10.1007/BF02936069
  13. A. Sapena, A contribution to the study of fuzzy metric spaces, Appl. Gen. Topol. 2 (2001), no. 1, 63-76. https://doi.org/10.4995/agt.2001.3016