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Journal of Function Spaces
Volume 2015, Article ID 919202, 6 pages
http://dx.doi.org/10.1155/2015/919202
Research Article

A Probabilistic Fixed Point Result Using Altering Distance Functions

1Department of Mathematics, West University of Timișoara, Bulevardul V. Pârvan 4, 300223 Timișoara, Romania
2Department of Mathematics, Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 74, 11000 Belgrade, Serbia

Received 26 February 2015; Accepted 3 August 2015

Academic Editor: Richard I. Avery

Copyright © 2015 Claudia Zaharia and Nataša Ćirović. 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.

Linked References

  1. K. Menger, “Statistical metrics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 28, pp. 535–537, 1942. View at Google Scholar
  2. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing, New York, NY, USA, 1983. View at MathSciNet
  3. G. Constantin and I. Istrăţescu, Elements of Probabilistic Analysis with Applications, Kluwer Academic Publishers, 1989.
  4. S. Romaguera, A. Sapena, and P. Tirado, “The Banach fixed point theorem in fuzzy quasi-metric spaces with application to the domain of words,” Topology and Its Applications, vol. 154, no. 10, pp. 2196–2203, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Romaguera and P. Tirado, “The complexity probabilistic quasi-metric space,” Journal of Mathematical Analysis and Applications, vol. 376, no. 2, pp. 732–740, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. J. Sun, X. Wu, V. Palade, W. Fang, C.-H. Lai, and W. Xu, “Convergence analysis and improvements of quantum-behaved particle swarm optimization,” Information Sciences, vol. 193, pp. 81–103, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. L. B. Ćirić, “On fixed points of generalized contractions on probabilistic metric spaces,” Publications de l'Institut Mathématique (Beograd), vol. 18, no. 32, pp. 71–78, 1975. View at Google Scholar
  8. B. S. Choudhury and K. Das, “A new contraction principle in Menger spaces,” Acta Mathematica Sinica, vol. 24, no. 8, pp. 1379–1386, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. D. Miheţ, “Altering distances in probabilistic Menger spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2734–2738, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. N. A. Babačev, “Nonlinear generalized contractions on Menger PM spaces,” Applicable Analysis and Discrete Mathematics, vol. 6, no. 2, pp. 257–264, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. B. S. Choudhury, K. Das, and P. N. Dutta, “A fixed point result in Menger spaces using a real function,” Acta Mathematica Hungarica, vol. 122, no. 3, pp. 203–216, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. O. Hadžić, “On the (ε,λ)-topology of probabilistic locally convex spaces,” Glasnik Matematicki. Serija III, vol. 13, no. 33, 2, pp. 293–297, 1978. View at Google Scholar
  13. V. M. Sehgal, Some fixed point theorems in functional analysis and probability [Ph.D. thesis], Wayne State University, 1966.
  14. O. Hadžić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, 2001.
  15. V. Radu, “On the t-norms of Hadžić type and fixed points in PM-spaces,” Review of Research (Novi Sad), vol. 13, pp. 81–86, 1983. View at Google Scholar
  16. M. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,” Bulletin of the Australian Mathematical Society, vol. 30, no. 1, pp. 1–9, 1984. View at Publisher · View at Google Scholar
  17. H. Sherwood, “Complete probabilistic metric spaces,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 20, no. 2, pp. 117–128, 1971. View at Publisher · View at Google Scholar · View at Scopus
  18. T. Došenović, P. Kumam, D. Gopal, D. K. Patel, and A. Takači, “On fixed point theorems involving altering distances in Menger probabilistic metric spaces,” Journal of Inequalities and Applications, vol. 2013, article 576, 10 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus