DOI QR코드

DOI QR Code

INVARIANT CONVERGENCE IN FUZZY NORMED SPACES

  • Yalvac, Seyma (Faculty of Education, Afyon Kocatepe University) ;
  • Dundar, Erdinc (Deparment of Mathematics, Afyon Kocatepe University)
  • 투고 : 2021.03.04
  • 심사 : 2021.04.01
  • 발행 : 2021.09.25

초록

In this study, we defined the notions of invariant convergence and invariant Cauchy sequences in fuzzy normed spaces. Also, we investigated some properties of invariant convergence and relations between invariant convergence and invariant Cauchy sequences in fuzzy normed spaces.

키워드

참고문헌

  1. T. Bag and S.K. Samanta, Fixed point theorems in Felbin's type fuzzy normed linear spaces, J. Fuzzy Math. 16(1) (2008), 243-260.
  2. S. Banach, Th'eorie des Operations Lineaires, Warszawa, (1932).
  3. C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24(1) (1968), 182-190. https://doi.org/10.1016/0022-247x(68)90057-7
  4. S.C. Cheng and J.N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, First International Conference on Fuzzy Theory and Technology Proceedings, Abstracts and Summaries, (1992), 193-197.
  5. N.R. Das and P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems, 107 (1999), 349-354. https://doi.org/10.1016/S0165-0114(97)00302-3
  6. D. Dean and R.A. Raimi, Permutations with comparable sets of invariant means, Duke Math. 27 (1960), 467-479.
  7. E. Dundar and O. Talo, $\mathcal{I}$-convergence of double sequences of fuzzy numbers, Iran. J. Fuzzy Syst. 10(3) (2013), 37-50.
  8. P. Diamond and P. Kloeden, Metric spaces of fuzzy sets-theory and aplications, World Scientific, Singapore, (1994).
  9. J.-X. Fang, A note on the completions of fuzzy metric spaces and fuzzy normed space, Fuzzy Sets and Systems, 131 (2002), 399-407. https://doi.org/10.1016/S0165-0114(02)00054-4
  10. J.-X. Fang and H.Huang, On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets and Systems, 147 (2004), 417-435.
  11. C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992), 293-248. https://doi.org/10.1016/0165-0114(92)90338-5
  12. A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Sytems, 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  13. R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986), 31-43. https://doi.org/10.1016/0165-0114(86)90026-6
  14. M. Itoh and M. Cho, Fuzzy bounded operators, Fuzzy Sets and Systems, 93 (1998), 353-362. https://doi.org/10.1016/S0165-0114(96)00198-4
  15. O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Sytems, 12 (1984), 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  16. A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12,, (1984), 143-154. https://doi.org/10.1016/0165-0114(84)90034-4
  17. I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5) (1975), 336-344.
  18. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190. https://doi.org/10.1007/BF02393648
  19. J. Michalek, Fuzzy topologies, Kybernetika, 11 (1975), 345-354.
  20. H.I. Miller and C. Orhan, On almost convergent and statistically convergent subsequences, Acta Math. Hungar. 93(1-2) (2001), 135-151. https://doi.org/10.1023/A:1013877718406
  21. M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22 (2009), 1700-1704. https://doi.org/10.1016/j.aml.2009.06.005
  22. M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford, 34 (1983), 77-86. https://doi.org/10.1093/qmath/34.1.77
  23. M. Mursaleen, Matrix transformations between some new sequence spaces, Houston J. Math. 9 (1983), 505-509.
  24. R.A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963), 81-94. https://doi.org/10.1215/S0012-7094-63-03009-6
  25. E. Savas, Some sequence spaces involving invariant means, Indian J. Math. 31 (1989), 1-8.
  26. E. Savas, Strong σ-convergent sequences, Bull. Calcutta Math. 81 (1989), 295-300.
  27. P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104-110. https://doi.org/10.1090/S0002-9939-1972-0306763-0
  28. C. Sencimen and S. Pehlivan, Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems, 159 (2008), 361-370. https://doi.org/10.1016/j.fss.2007.06.008
  29. J. Xiao and X. Zhu, On linearly topological structure and property of fuzzy normed linear space, Fuzzy Sets and Systems, 125 (2002), 153-161. https://doi.org/10.1016/S0165-0114(00)00136-6
  30. L.A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X