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  • Research Article
  • Open Access

On Fuzzy -Contractive Mappings in Fuzzy Metric Spaces

Fixed Point Theory and Applications20072007:087471

https://doi.org/10.1155/2007/87471

  • Received: 24 December 2006
  • Accepted: 1 March 2007
  • Published:

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

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Authors’ Affiliations

(1)
Faculty of Mathematics and Computer Science, West University of Timişoara, Bv. V. Parvan 4, Timişoara, 300223, Romania

References

  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)90162-7MathSciNetView ArticleMATHGoogle Scholar
  2. Gregori V, Romaguera S: Characterizing completable fuzzy metric spaces. Fuzzy Sets and Systems 2004,144(3):411–420. 10.1016/S0165-0114(03)00161-1MathSciNetView ArticleMATHGoogle Scholar
  3. Razani A: A contraction theorem in fuzzy metric spaces. Fixed Point Theory and Applications 2005,2005(3):257–265. 10.1155/FPTA.2005.257MathSciNetView ArticleMATHGoogle Scholar
  4. Grabiec M: Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems 1988,27(3):385–389. 10.1016/0165-0114(88)90064-4MathSciNetView ArticleMATHGoogle Scholar
  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. Radu V: Some suitable metrics on fuzzy metric spaces. Fixed Point Theory 2004,5(2):323–347.MathSciNetMATHGoogle Scholar
  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

© 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.

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