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COMPATIBLE MAPS OF TWO TYPES AND COMMON FIXED POINT THEOREMS ON INTUITIONISTIC FUZZY METRIC SPACE

  • Park, Jong-Seo (Department of Mathematics Education, Chinju National University of Education)
  • Received : 2010.02.17
  • Accepted : 2010.05.31
  • Published : 2010.06.25

Abstract

In this paper, we introduce the concept of compatible mapping of type(${\alpha}$-1) and type(${\alpha}$-2), prove the some properties and common fixed point theorem for such maps in intuitionistic fuzzy metric space. Also, we give the example. Our research are an extension for the results of Kutukcu and Sharma[3] and Park et.al.[11].

Keywords

References

  1. Cho, Y.J., Pathak, H.K., Kang, S.M., Jung, J.S., 1998. Common fixed points of compatible maps of type($\beta$) on fuzzy metric spaces. Fuzzy Sets and Systems 93, 99-111. https://doi.org/10.1016/S0165-0114(96)00200-X
  2. Kramosil,J., Michalek J., 1975. Fuzzy metric and statistical metric spaces. Kybernetica 11, 326-334.
  3. Kutukcu, S., Sharma, S., 2009. Compatible maps and common fixed points in Menger probabilistic metric spaces. Commun. Korean Math. Soc. 24(1), 17-27. https://doi.org/10.4134/CKMS.2009.24.1.017
  4. Park, J.H., 2004. Intuitionistic fuzzy metric spaces. Chaos Solitons & Fractals 22(5), 1039-1046. https://doi.org/10.1016/j.chaos.2004.02.051
  5. Park, J.H., Park, J.S., Kwun, Y.C., 2006. A common fixed point theorem in the intuitionistic fuzzy metric space. Advances in Natural Comput. Data Mining(Proc. 2nd ICNC and 3rd FSKD), 293-300.
  6. Park, J.H., Park, J.S., Kwun, Y.C., 2007. Fixed point theorems in intuitionistic fuzzy metric space(I). JP J. fixed point Theory & Appl. 2(1), 79-89.
  7. Park, J.H., Park, J.S., Kwun, Y.C., 2007. Fixed points M-fuzzy metric spaces. Advanced in soft computing. 40, 206-215. https://doi.org/10.1007/978-3-540-71441-5_23
  8. Park, J.S., Kim, S.Y., 1999. A fixed point theorem in a fuzzy metric space. F.J.M.S. 1(6), 927-934.
  9. Park, J.S., Kwun, Y.C., 2007. Some fixed point theorems in the intuitionistic fuzzy metric spaces. F.J.M.S. 24(2) 227-239.
  10. Park, J.S., Kwun, Y.C., Park, J.H., 2005. A fixed point theorem in the intuitionistic fuzzy metric spaces. F.J.M.S. 16(2), 137-149.
  11. Park J.S., Park, J.H., Kwun, Y.C., 2008. On some results for five mappings using compatibility of type($\alpha$) in intuitionistic fuzzy metric space. Internat. J. KIIS. 8(4), 299-305.
  12. Schweizer, B., Sklar, A., 1960. Statistical metric spaces. Pacific J. Math. 10, 314-334.
  13. Sharma, S., 2002. Common fixed point theorems in fuzzy metric spaces. Fuzzy Sets and Systems 127, 345-352. https://doi.org/10.1016/S0165-0114(01)00112-9
  14. Zadeh, L.A., 1965. Fuzzy sets. Inform. and Control 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X