Skip to main content
Log in

A note on a common fixed point theorem in probabilistic metric spaces

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

In the recent paper [1] the claim is made that a probabilistic version of a common fixed point theorem of Pant holds. We provide some examples to demonstrate that this claim is false unless some additional conditions are imposed. Our note is desired to complete the interesting results in the quoted paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. K. Kohli and S. Vashista, Common fixed points theorems in probabilistic metric spaces, Acta Math. Hungar., 115 (2007), 37–47, DOI: 10.1007/s10474-006-0533-7.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Miheţ, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008), 739–744.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188 (1994), 436–440.

    Article  MATH  MathSciNet  Google Scholar 

  4. H. K. Pathak and P. Singh, Common fixed point theorem for weakly compatible mappings, International Mathematical Forum, 2 (2007), 2831–2839.

    MATH  MathSciNet  Google Scholar 

  5. V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Math. Systems Theory, 6 (1972), 97–102.

    Article  MATH  MathSciNet  Google Scholar 

  6. T. Som, Some results in common fixed points in fuzzy metric spaces, Sookhow Journal of Mathematics, 33 (2007), 553–561.

    MATH  MathSciNet  Google Scholar 

  7. D. Turkoglu, C. Alaca, Y. J. Cho and C. Yildiz, Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Appl. Math. & Computing, 22 (2006), 411–424.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Vasuki and P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric spaces, Fuzzy Sets and Systems, 135 (2003), 409–413.

    Article  MathSciNet  Google Scholar 

  9. R. Vasuki, Common fixed points for R-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math., 30 (1999), 419–423.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. Miheţ.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miheţ, D. A note on a common fixed point theorem in probabilistic metric spaces. Acta Math Hung 125, 127–130 (2009). https://doi.org/10.1007/s10474-009-8238-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-009-8238-3

Key words and phrases

2000 Mathematics Subject Classification

Navigation