Existence and Uniqueness of Fixed Point in Fuzzy Metric Spaces and its Applications

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 236)

Abstract

The main aim of this paper is to prove some fixed point theorems in fuzzy metric spaces through rational inequality. Our results extend and generalize the results of many other authors existing in the literature. Some applications are also given in support of our results.

Keywords

Fuzzy metric space Rational expression Integral type Control function 

Notes

Acknowledgments

The authors would like to express their sincere appreciation to the referees for their helpful suggestions and many kind comment.

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Kramosil, O., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybornetica 11, 326–334 (1975)MathSciNetGoogle Scholar
  3. 3.
    Grabeic, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1988)CrossRefGoogle Scholar
  4. 4.
    George, A., Veermani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395–399 (1994)CrossRefMATHGoogle Scholar
  5. 5.
    Balasubramaniam, P., Murlisankar, S., Pant, R.P.: Common fixed points of four mappings in a fuzzy metric space. J. Fuzzy Math. 10(2), 379–384 (2002)MATHMathSciNetGoogle Scholar
  6. 6.
    Cho, S.H.: On common fixed point theorems in fuzzy metric spaces. Int. Math. Forum 1(9–12), 471–479 (2006)Google Scholar
  7. 7.
    Cho, Y.J., Sedghi, S., Shobe, N.: Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces. Chaos, Solitons and Fractals 39, 2233–2244 (2009)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Gregori, V., Sapena, A.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 125, 245–252 (2002)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Mishra, S.N., Sharma, S.N., Singh, S.L.: Common fixed point of maps on fuzzy metric spaces. Internat. J. Math. Sci 17, 253–258 (1994)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Saini, R.K., Gupta, V.: Common coincidence points of R-Weakly commuting fuzzy maps, thai journal of mathematics, mathematical assoc. of Thailand, 6(1):109–115, (2008) ISSN 1686–0209.Google Scholar
  11. 11.
    Saini, R.K., Gupta, V.: Fuzzy version of some fixed points theorems on expansion type maps in fuzzy metric space. Thai J. Math., Math. Assoc. Thailand 5(2), 245–252 (2007). ISSN 1686–0209MATHMathSciNetGoogle Scholar
  12. 12.
    Vasuki, R.: A common fixed point theorem in a fuzzy metric space. Fuzzy Sets and Syst. 97, 395–397 (1998)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Vasuki, R.: Common fixed point for R-weakly commuting maps in fuzzy metric space. Indian J. Pure. Appl. Math. 30, 419–423 (1999)MATHMathSciNetGoogle Scholar
  14. 14.
    Schweizer, B., Sklar, A.: Probabilistic metric spaces, North-Holland series in probability and applied mathematics. North-Holland Publishing Co., New York (1983), ISBN: 0-444-00666-4 MR0790314 (86g:54045).Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of MathematicsMaharishi Markandeshwar UniversityMullana AmbalaIndia

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