Common Coupled Fixed Point Results in Fuzzy Metric Spaces Using JCLR Property

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 43)

Abstract

The present study is devoted to use the notion of joint common limit (shortly, \(JCLR\) property) for coupled maps and utilize this concept to prove common coupled fixed point theorem on fuzzy metric space. In this paper, we also prove some fixed point theorems using the concept \(CLR\) property, E.A property and integral type contractive condition in fuzzy metric space. Illustrative examples supporting main results have been given.

Keywords

Fixed point Fuzzy metric space Weakly compatible mappings E.A property \(CLR\) property \(JCLR\) property 

References

  1. 1.
    Zadeh, L.A.: Fuzzy Sets. Inform. Control‚ 8, 338–353 (1965)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Kramosil, I., Michalek, J.: Fuzzy metric and Statistical metric spaces, Kybernetica, 11, 326–334 (1995)Google Scholar
  3. 3.
    George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 336–344 (1994)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bhaskar, T.G., Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. TMA. 65, 1379–1393 (2006)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Lakshmikantham, V., Ćirić, LjB: Coupled fixed point theorems for nonlinear contractions in partially ordered metric space. Nonlinear Anal. TMA. 70, 4341–4349 (2009)MATHCrossRefGoogle Scholar
  6. 6.
    Abbas, M., Ali Khan, M., Radenovic, S.: Common coupled fixed point theorems in cone metric spaces for w-compatible mappings. Appl. Math. Comput. 217, 195–202 (2010)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Aamri, M., Moutawakil, D.E.I.: Some new common fixed point theorems under strict Contractive conditions. J. Math. Anal. Appl. 270, 181–188 (2002)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Sintunavarat, W., Kuman, P.: Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. Article ID: 637958 (2011)Google Scholar
  9. 9.
    Branciari, A.: A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Sci. 29, 531–536 (2000)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ćirić, L.j.: Common fixed point theorems for a family of non-self mappings in convex metric spaces. Nonlinear Anal. 71, 1662–1669 (2009)Google Scholar
  11. 11.
    Deng, Z.: Fuzzy pseudometric spaces. J. Math. Anal. Appl. 86, 74–95 (1982)MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Gupta, V., Kanwar, A.: Fixed point theorem in fuzzy metric spaces satisfying E.A. property, Indian. J. Sci. Technol. 5, 3767–3769 (2012)Google Scholar
  13. 13.
    Hu, X.-Q.: Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces, Fixed Point Theor. Appl. Article ID 363716 (2011)Google Scholar
  14. 14.
    Mishra, S.N., Sharma, N., Singh, S.L.: Common fixed points of maps on fuzzy metric spaces. Int. J. Math. Sci. 17, 253–258 (1994)MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Schweizer, B., Sklar, A.: Statistical metric spaces, Pacific J. Math. 10, 314–334 (1960)Google Scholar
  16. 16.
    Kumar, S., Singh, B., Gupta, V., Kang, S.M.: Some Common Fixed Point Theorems for weakly compatible mappings in fuzzy metric spaces. Int. J. Math. Anal. 8, 571–583 (2014)MathSciNetGoogle Scholar

Copyright information

© Springer India 2016

Authors and Affiliations

  1. 1.Maharishi Markandeshwar UniversityAmbalaIndia
  2. 2.S.D CollegeAmbalaIndia

Personalised recommendations