Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

HAUSDORFF TOPOLOGY INDUCED BY THE FUZZY METRIC AND THE FIXED POINT THEOREMS IN FUZZY METRIC SPACES

  • WU, HSIEN-CHUNG (DEPARTMENT OF MATHEMATICS NATIONAL KAOHSIUNG NORMAL UNIVERSITY)
  • Received : 2015.01.14
  • Published : 2015.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

The Hausdorff topology induced by a fuzzy metric space under more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy metric space based on a natural concept of Cauchy sequence in fuzzy metric space.

Keywords

References

  1. C. Alaca, D. Turkoglu, and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 29 (2006), no. 5, 1073-1078. https://doi.org/10.1016/j.chaos.2005.08.066
  2. S. S. Chang, Y. J. Cho, and S. M. Kang, Nonlinear operator theory in probabilistic metric space, Nova Science Publishers, New York, 2001.
  3. 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
  4. A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems 90 (1997), no. 3, 365-368. https://doi.org/10.1016/S0165-0114(96)00207-2
  5. 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
  6. V. Gregori and S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems 130 (2002), no. 3, 399-404. https://doi.org/10.1016/S0165-0114(02)00115-X
  7. V. Gregori, S. Romaguera, and A. Sapena, A note on intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 28 (2006), no. 4, 902-905. https://doi.org/10.1016/j.chaos.2005.08.113
  8. V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), no. 2, 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9
  9. O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Klumer Academic Publishers, 2001.
  10. 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
  11. I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), no. 5, 336-344.
  12. B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334. https://doi.org/10.2140/pjm.1960.10.313
  13. B. Schweizer and A. Sklar, Triangle inequalities in a class of statistical metric spaces, J. London Math. Soc. 38 (1963), 401-406.
  14. B. Schweizer, A. Sklar, and E. Thorp, The metrization of statistical metric spaces, Pacific J. Math. 10 (1960), 673-675. https://doi.org/10.2140/pjm.1960.10.673
  15. S. Sharma and B. Deshpande, Common fixed point theorems for finite numbers of map-pings without continuity and compatibility on intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 40 (2009), no. 5, 2242-2256. https://doi.org/10.1016/j.chaos.2007.10.011
  16. G. Song, Comments on "A common fixed point theorem in a fuzzy metric space", Fuzzy Sets and Systems 135 (2003), no. 3, 409-413. https://doi.org/10.1016/S0165-0114(02)00131-8
  17. P. V. Subrahmanyam, A common fixed point theorem in fuzzy metric spaces, Inform. Sci. 83 (1995), no. 3-4, 109-112. https://doi.org/10.1016/0020-0255(94)00043-B
  18. R. Vasuki and P. Veeramani, Fixed point theorems and cauchy sequences in fuzzy metric spaces, Fuzzy Sets and Systems 135 (2003), no. 3, 415-417. https://doi.org/10.1016/S0165-0114(02)00132-X

Cited by

  1. Convergence in Fuzzy Semi-Metric Spaces vol.6, pp.9, 2018, https://doi.org/10.3390/math6090170
  2. Fuzzy Semi-Metric Spaces vol.6, pp.7, 2018, https://doi.org/10.3390/math6070106
  3. Near Fixed Point Theorems in the Space of Fuzzy Numbers vol.6, pp.7, 2018, https://doi.org/10.3390/math6070108
  4. Common Coincidence Points and Common Fixed Points in Fuzzy Semi-Metric Spaces vol.6, pp.2, 2018, https://doi.org/10.3390/math6020029