DOI QR코드

DOI QR Code

COMMON FIXED POINT THEOREMS WITHOUT CONTINUITY AND COMPATIBILITY IN INTUITIONISTIC FUZZY METRIC SPACE

  • Park, Jong-Seo (Department of Mathematics Education, Chinju National University of Education)
  • Received : 2011.02.17
  • Accepted : 2011.04.12
  • Published : 2011.06.25

Abstract

In this paper, we prove some common fixed point theorems for finite number of discontinuous, non-compatible mapping on non-complete intuitionistic fuzzy metric spaces and obtain the example. Our research improve, extend and generalize several known results in intuitionistic fuzzy metric spaces.

Keywords

References

  1. Jungck, G., Rhoades, B.E., 1998. Fixed point for set valued functions without continuity, Ind. J. Pure Appl. Math. 29(3), 227-238.
  2. Kaleva, O., Seikkala, S., 1984. On fuzzy metric spaces, Fuzzy Sets and Systems 12, 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  3. Kramosil,J., Michalek J., 1975. Fuzzy metric and statistical metric spaces. Kybernetica 11, 326-334.
  4. 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.
  5. 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.
  6. Park, J.S., On some results for five mappings using compatibility of type($\alpha$) in a fuzzy metric space, inpress.
  7. Park, J.S., Kim, S.Y., 1999. A fixed point theorem in a fuzzy metric space. F.J.M.S. 1(6), 927-934.
  8. 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.
  9. 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.
  10. Park, J.S., Kwun, Y.C., Park, J.H., Some results and example for compatible maps of type($\beta$) on the intuitionistic fuzzy metric spaces, inpress.
  11. Schweizer, B., Sklar, A., 1960. Statistical metric spaces. Pacific J. Math. 10, 314-334.
  12. Sessa, S., 1982. On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. 32(46), 149-153.
  13. Sharma, S., Desphaude, B., Tiwari, R., 2008. Common fixed point theorems for finite number of mappings without continuity and compatibility in Menger spaces, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 15(2), 135-151.