Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

A common fixed point theorem in the intuitionistic fuzzy metric space

  • Park Jong-Seo (Department of Mathematics Education, Chinju National University) ;
  • Kim Seon-Yu (Department of Mathematics Education, Chinju National University) ;
  • Kang Hong-Jae (Department of Mathematics Education, Chinju National University)
  • Published : 2006.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to establish the common fixed point theorem in the intuitionistic fuzzy metric space in which it is a little revised in Park [11]. Our research are an extension of Jungck's common fixed point theorem [8] in the intuitionistic fuzzy metric space.

Keywords

References

  1. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96 https://doi.org/10.1016/S0165-0114(86)80034-3
  2. K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61 (1994), 137-142 https://doi.org/10.1016/0165-0114(94)90229-1
  3. K. Atanassov and S. Stoeva, Intuitionistic fuzzy sets, in:Polish Symp. on Interval and Fuzzy Mathematics, Poznan(August), (1986), 23-26
  4. D. Coker, On fuzzy inclusion in intuitionistic sense, J. Fuzzy Math., 4 (1996), 701-714
  5. M. Edelstein, On fixed point and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74-79 https://doi.org/10.1112/jlms/s1-37.1.74
  6. M. Grabiec, Fixed point in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389 https://doi.org/10.1016/0165-0114(88)90064-4
  7. G. Jungck, Commutating maps and fixed points, Amer. Math. Monthly, 83 (1976), 261-263 https://doi.org/10.2307/2318216
  8. G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771-774 https://doi.org/10.1155/S0161171286000935
  9. J. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), 326-334
  10. R. Lowen, Convergence in fuzzy topological spaces, General Topology and its Applns., 10 (1979), 147-160 https://doi.org/10.1016/0016-660X(79)90004-7
  11. J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5) (2004), 1039-1046 https://doi.org/10.1016/j.chaos.2004.02.051
  12. J. S. Park and S. Y. Kim, A fixed point Theorem in a fuzzy metric space, F. J. M. S., 1(6) (1999), 927-934
  13. J. S. Park, Y. C. Kwun and J. H. Park, A fixed point theorem in the intuitionistic fuzzy metric spaces, F. J. M. S. 16(2) (2005), 137-149
  14. B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 314-334
  15. B. Schweizer and A. Sklar, Probabilistic metric spaces, North-Holland, New York, Oxford, (1983)
  16. P. V. Subrahmanyam, A common fixed point theorem in fuzzy metric spaces, Inform. Sci., 83 (1995), 109-112 https://doi.org/10.1016/0020-0255(94)00043-B
  17. 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. Fixed points in $${\mathcal{M}}$$ -fuzzy metric spaces vol.7, pp.4, 2008, https://doi.org/10.1007/s10700-008-9039-9