Fixed Point Theory and Applications

, 2007:087471 | Cite as

On Fuzzy Open image in new window -Contractive Mappings in Fuzzy Metric Spaces

Open Access
Research Article

Abstract

We answer into affirmative an open question raised by A. Razani in 2005. An essential role in our proofs is played by the separation axiom in the definition of a fuzzy metric space in the sense of George and Veeramani.

Keywords

Essential Role Differential Geometry Computational Biology Separation Axiom 

References

  1. [1]
    George A, Veeramani P: On some results in fuzzy metric spaces. Fuzzy Sets and Systems 1994,64(3):395–399. 10.1016/0165-0114(94)90162-7MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Gregori V, Romaguera S: Characterizing completable fuzzy metric spaces. Fuzzy Sets and Systems 2004,144(3):411–420. 10.1016/S0165-0114(03)00161-1MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Razani A: A contraction theorem in fuzzy metric spaces. Fixed Point Theory and Applications 2005,2005(3):257–265. 10.1155/FPTA.2005.257MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Grabiec M: Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems 1988,27(3):385–389. 10.1016/0165-0114(88)90064-4MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Schweizer B, Sklar A: Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics. North-Holland, New York, NY, USA; 1983:xvi+275.Google Scholar
  6. [6]
    Radu V: Some suitable metrics on fuzzy metric spaces. Fixed Point Theory 2004,5(2):323–347.MathSciNetMATHGoogle Scholar
  7. [7]
    Ćirić L, Ješić S, Ume JS: The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces. to appear in Chaos, Solitons & FractalsGoogle Scholar

Copyright information

© Dorel Miheţ 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceWest University of TimişoaraTimişoaraRomania

Personalised recommendations