Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

WEAKLY CONVERGENT SEQUENCES IN FUZZY NORMED SPACES

  • Cho, Kyugeun (Bangmok College of General Education, Myong Ji University)
  • Received : 2021.02.28
  • Accepted : 2021.09.21
  • Published : 2021.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce the definition of weakly convergent sequence in fuzzy normed spaces. We investigate relationship between convergent sequence and weakly convergent sequence in fuzzy normed spaces. We also study the dual spaces of a standard fuzzy normed space and 01-fuzzy normed space.

Keywords

Acknowledgement

The author is grateful to the referee for very valuable comments and suggestions.

References

  1. C. Alegre, S. Romaguera, The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited, Abstr. Appl. Anal. 2014 (2014), Art. ID 151472.
  2. T. Bag, S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), 687-705.
  3. T. Bag, S. K. Samanta, Fuzzy bounded linear operators in felbin's type fuzzy normed linear spaces, Fuzzy Sets Syst. 151 (2005), 513-547. https://doi.org/10.1016/j.fss.2004.05.004
  4. K. Cho, C. Lee, On convergences in fuzzy normed spaces, Far East J. Math. Sci. 109 (2018), 129-141. https://doi.org/10.17654/ms109010129
  5. K. Cho, C. Lee, Some results on convergences in fuzzy metric spaces and fuzzy normed spaces, Commun. Korean Math. Soc. 35 (2020), 185-199. https://doi.org/10.4134/CKMS.c180460
  6. C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets Syst. 48 (1992), 239-248. https://doi.org/10.1016/0165-0114(92)90338-5
  7. R. Saadati, S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput. 17 (2005), 475-484. https://doi.org/10.1007/BF02936069
  8. J. Simon, Banach, Frechet, Hilbert and Neumann Spaces, John Wiley & Sons, Hoboken, 2017.