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A LOCAL FIXED POINT THEOREM ON FUZZY METRIC SPACES

  • Sedghi, Shaban ;
  • Altun, Ishak ;
  • Shobe, Nabi
  • Received : 2010.11.02
  • Published : 2012.04.30

Abstract

In this paper, we present a common fixed point theorem for multivalued maps on $M$-complete fuzzy metric spaces. Also, the single valued case and an illustrative example are given.

Keywords

fixed point;fuzzy metric space;multivalued map

References

  1. A. Aliouche, F. Merghadi, and A. Djoudi, A related fixed point theorem in two fuzzy metric spaces, J. Nonlinear Sci. Appl. 2 (2009), no. 1, 19-24.
  2. I. Altun, Some fixed point theorems for single and multi valued mappings on ordered non-Archimedean fuzzy metric spaces, Iran. J. Fuzzy Syst. 7 (2010), no. 1, 91-96.
  3. I. Altun and D. Mihet, Ordered non-Archimedean fuzzy metric spaces and some fixed point results, Fixed Point Theory Appl. 2010 (2010), 11pages.
  4. Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math. 5 (1997), no. 4, 949-962.
  5. J. X. Fang, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 46 (1992), no. 1, 107-113. https://doi.org/10.1016/0165-0114(92)90271-5
  6. A. George and P. Veeramani, On some result in fuzzy metric space, 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 and A. Sapena, On fixed-point theorem 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, Kluwer Academic Publishers, Dordrecht, 2001.
  10. S. Jain, S. Jain, and L. Bahadur, Compatibility of type (P) in modified intuitionistic- fuzzymetric space, J. Nanlinear Sci. Appl. 3 (2010), no. 2, 96-109.
  11. D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems 158 (2007), no. 8, 915-921. https://doi.org/10.1016/j.fss.2006.11.012
  12. D. Mihet, Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008), no. 6, 739-744. https://doi.org/10.1016/j.fss.2007.07.006
  13. S. N. Mishra, S. N. Sharma, and S. L. Singh, Common fixed points of maps on fuzzy metric spaces, Internat. J. Math. Math. Sci. 17 (1994), no. 2, 253-258. https://doi.org/10.1155/S0161171294000372
  14. V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, Automat. Comput. Appl. Math. 11 (2002), no. 1, 125-131.
  15. K. P. R. Rao, A. Aliouche, and G. R. Babu, Related fixed point theorems in fuzzy metric spaces, J. Nonlinear Sci. Appl. 1 (2008), no. 3, 194-202.
  16. J. L. Rodriguez and S. Ramaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems 147 (2004), no. 2, 273-283. https://doi.org/10.1016/j.fss.2003.09.007
  17. B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334. https://doi.org/10.2140/pjm.1960.10.313
  18. S. Sedghi, N. Shobe, and I. Altun, A fixed fuzzy point for fuzzy mappings in complete metric spaces, Math. Commun. 13 (2008), no. 2, 289-294.
  19. S. Sedghi, I. Altun, and N. Shobe, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Anal. 72 (2010), no. 3-4, 1298-1304. https://doi.org/10.1016/j.na.2009.08.018
  20. T. Zikic-Dosenovic, A common fixed point theorem for compatible mappings in fuzzy metric spaces using implicit relation, Acta Math. Hungar 125 (2009), no. 4, 357-368. https://doi.org/10.1007/s10474-009-9029-6