Fixed Points in Non-Archimedean Fuzzy Metric Spaces

  • Yeol Je Cho
  • Themistocles M. Rassias
  • Reza Saadati


Recently, Miheţ enlarged the class of fuzzy contractive mappings of Gregori and Sapena and proved a fuzzy Banach contraction result in complete non-Archimedean fuzzy metric spaces.


  1. 9.
    I. Altun, D. Miheţ, Ordered non-Archimedean fuzzy metric spaces and some fixed point results. Fixed Point Theory Appl. 2010, 11 pp., Article ID 782680 (2010)Google Scholar
  2. 10.
    I. Altun, Some fixed point theorems for single and multi valued mappings on ordered non-Archimedean fuzzy metric spaces. Iran. J. Fuzzy Syst. 7, 91–96 (2010)MathSciNetzbMATHGoogle Scholar
  3. 14.
    J.V. Armitage, J.R. Parker, Jorgensen’s inequality for non-Archimedean metric spaces, in Geometry and Dynamics of Groups and Spaces. Progress in Mathematics, vol. 265 (Birkhauser, Basel, 2008), pp. 97–111Google Scholar
  4. 17.
    H. Aydi, E. Karapinar, Fixed point results for generalized α-ψ-contractions in metric-like spaces and applications. Electr. J. Differ. Equ. 133, 1–15 (2015)MathSciNetGoogle Scholar
  5. 18.
    H. Aydi, A. Felhi, S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces. Math. Sci. 9, 103–108 (2015)MathSciNetCrossRefGoogle Scholar
  6. 30.
    J. Caristi, Fixed point theory and inwardness conditions, in Applied Nonlinear Analysis (Proceedings of Third International Conference, University of Texas, Arlington, TX, (1978)) (Academic, New York, 1979), pp. 479–483Google Scholar
  7. 52.
    A. George, P. Veeramani, On some result in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395–399 (1994)MathSciNetCrossRefGoogle Scholar
  8. 53.
    A. George, P. Veeramani, On some result of analysis for fuzzy metric spaces. Fuzzy Sets Syst. 90, 365–368 (1997)MathSciNetCrossRefGoogle Scholar
  9. 56.
    M. Grabiec, Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385—389 (1988)MathSciNetCrossRefGoogle Scholar
  10. 57.
    M. Grabiec, Fixed point in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1989)MathSciNetCrossRefGoogle Scholar
  11. 62.
    V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 125, 245–252 (2002)CrossRefGoogle Scholar
  12. 74.
    A. Hierro, M.D. Sen, Some fixed point theorems in Menger probabilistic metric-like spaces. Fixed Point Theory Appl. 2015, 176 (2015)MathSciNetCrossRefGoogle Scholar
  13. 79.
    V. Istratescu, An Introduction to Theory of Probabilistic Metric Spaces with Applications (Tehnica, Bucuresti, 1974, in Romanian)Google Scholar
  14. 92.
    M.A. Khamsi, Remarks on Caristi’s fixed point theorem. Nonlinear Anal. 71, 227–231 (2009)MathSciNetCrossRefGoogle Scholar
  15. 111.
    D. Miheţ, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets Syst. 159, 739–744 (2008)MathSciNetCrossRefGoogle Scholar
  16. 120.
    H.K. Pathak, N. Hussain, Common fixed points for Banach operator pairs with applications. Nonlinear Anal. 69, 2788–2802 (2008)MathSciNetCrossRefGoogle Scholar
  17. 122.
    V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces. Autom. Comput. Appl. Math. 11, 125–131 (2002)MathSciNetGoogle Scholar
  18. 142.
    Y.H. Shen, D. Qiu, W. Chen, Fixed point theorems in fuzzy metric spaces. Appl. Math. Lett. 25, 138–141 (2012)MathSciNetCrossRefGoogle Scholar
  19. 146.
    C. Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces. Fuzzy Sets Syst. 162, 84–90 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Yeol Je Cho
    • 1
    • 2
  • Themistocles M. Rassias
    • 3
  • Reza Saadati
    • 4
  1. 1.Department of Mathematical EducationGyeongsang National UniversityJinjuKorea (Republic of)
  2. 2.School of Mathematical ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Department of MathematicsNational Technical University of AthensAthensGreece
  4. 4.Department of MathematicsIran University of Science and TechnologyTehranIran

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