Common Fixed Points of Weakly Compatible Mappings in ~-Chainable Intuitionistic Fuzzy Metric Spaces

  • Authors

    • Seema Mehra Department of Mathematics, M.D.University, Rohtak, India
    https://doi.org/10.14419/ijet.v1i1.24

    Received date: April 13, 2012

    Accepted date: April 13, 2012

    Published date: April 13, 2012

  • Abstract

    The aim of this paper is to introduce the notion of -chainable intuitionistic fuzzy metric spaces and prove a common fixed point theorem for four weakly compatible mappings in this newly defined space. Our result is intuitionistic fuzzy version of Cho and Jung's [1] and Mukherjee's [9] results in -chainable fuzzy metric space.

  • References

    1. Cho, S.H., Jung, J.H., “On common fixed point theorems in fuzzy metric spaces”, International Mathematical Forum, Vol 1, No. 29, (2006), pp.1441-1451.
    2. Erceg, M.A., “Metric spaces in fuzzy set theory”, J. Math. Anal. Appl., Vol 69, (1979), pp. 205-230.
    3. George, A., Veeramani, P., “On some results in fuzzy metirc spaces”, Fuzzy Sets and Systems, Vol 64, (1994), pp. 395-399.
    4. George, A., Veeramani, P., “On some results of analysis for fuzzy metric Spaces”, Fuzzy Sets and Systems, Vol 90, (1997), pp. 365-368.
    5. Grabiec, M., “Fixed point in fuzzy metric spaces”, Fuzzy Sets and Systems, Vol 27, (1988), pp.385-389.
    6. Greogori, V., Romoguera, S., “On completion of fuzzy metric spaces”, Fuzzy Sets and Systems, Vol 130, (2002), pp. 399-404.
    7. Jungck, G., “Compatible mappings and fixed points”, Internat. J. Math. Math. Sci., Vol 9, No. 4(1986), pp. 771-779.
    8. Kramosil, O., Michalek, J., “Fuzzy metric and statistical metric spaces”, Kybernetica, Vol 11, (1975), pp. 326-334.
    9. Mukherjee, R.N., “On some fixed point theorems”, Kyungpook Math. J., Vol 14, (1974), pp. 37-44.
    10. Park, J.H., “Intuitionistic fuzzy metric spaces”, Chaos, Solitons and Fractals, Vol 22, (2004), pp. 1039-1046.
    11. Park, J. S., Kim, S.Y., “A fixed point theorem in a fuzzy metric space”, Far East J. Math. Sci. (FJMS), Vol 1, No. 6, (1999), pp. 927-934.
    12. Schweizer, B., Sklar, A., “Probabilistic Metric Spaces”, North-Holland, New York, Oxford, 1983.
    13. Singh, B., Chauhan, M.S., “Common fixed points of compatible maps in fuzzy metric spaces”, Fuzzy Sets and Systems, Vol 115, (2000), pp. 471-475.
    14. Vijayaraju, P., Marudai, M., “Fixed point theorems in fuzzy metric spaces”, J. Fuzzy Math., Vol 8, No. 2, (2000), pp. 867-871.
    15. Zadeh, L.A., “Fuzzy sets”, Inform. and Control, Vol 8(1965), pp. 338-353.

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  • How to Cite

    Mehra, S. (2012). Common Fixed Points of Weakly Compatible Mappings in ~-Chainable Intuitionistic Fuzzy Metric Spaces. International Journal of Engineering and Technology, 1(1), 14-25. https://doi.org/10.14419/ijet.v1i1.24