Table of Contents
International Journal of Computational Mathematics
Volume 2016, Article ID 7109190, 14 pages
http://dx.doi.org/10.1155/2016/7109190
Research Article

-Tupled Coincidence Point Theorems for Probabilistic -Contractions in Menger Spaces

Department of Pure and Applied Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh 495009, India

Received 14 July 2015; Revised 22 September 2015; Accepted 18 October 2015

Academic Editor: Don Hong

Copyright © 2016 Penumarthy Parvateesam Murthy and Uma Devi Patel. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. Schweizer and A. Sklar, Pobabilistic Metric Spaces, North-Holland, Amsterdam, The Netherlands, 1983.
  3. Y. Liu and Z. Li, “Coincidence point theorems in probabilistic and fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 158, no. 1, pp. 58–70, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. B. Schweizer and A. Sklar, “Statistical metric spaces,” Pacific Journal of Mathematics, vol. 10, pp. 313–334, 1960. View at Publisher · View at Google Scholar · View at MathSciNet
  5. B. Schweizer, A. Sklar, and E. Thorp, “The metrization of statistical metric spaces,” Pacific Journal of Mathematics, vol. 10, pp. 673–675, 1960. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. V. M. Sehgal and A. T. Bharucha-Reid, “Fixed points of contraction mappings on probabilistic metric spaces,” Mathematical Systems Theory, vol. 6, no. 1, pp. 97–102, 1972. View at Google Scholar · View at MathSciNet
  7. J.-X. Fang, “Common fixed point theorems of compatible and weakly compatible maps in Menger spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 5-6, pp. 1833–1843, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. O. Hadzic and E. Pap, Fixed Point Theory in Complete Metic Spaces, Kluwer Academic, Dordrecht, The Netherlands, 2001.
  9. J. X. Fang, “Fixed point theorems of local contraction mappings on Menger spaces,” Applied Mathematics and Mechanics, vol. 12, no. 4, pp. 363–372, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. J. Z. Xiao, X. H. Zhu, and Y. F. Cao, “Common coupled fixed point results for probabilistic ψ-contractions in Menger spaces,” Nonlinear Analysis, vol. 74, pp. 4589–4600, 2011. View at Google Scholar
  11. J. Jachymski, “On probabilistic ψ-contractions on Menger spaces,” Nonlinear Analysis—Theory, Methods & Applications, vol. 73, no. 7, pp. 2199–2203, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. M. Imdad, A. H. Soliman, B. S. Choudhury, and P. Das, “On n-tupled coincidence and common fixed points results in metric spaces,” Journal of Operators, vol. 2013, Article ID 532867, 8 pages, 2013. View at Publisher · View at Google Scholar
  13. B. Samet and C. Vetro, “Coupled fixed point, f-invarient set and fixed point of N-order,” Annals of Functional Analysis, vol. 1, no. 2, pp. 4656–4662, 2010. View at Google Scholar
  14. M. Imdad, A. Sharma, and K. P. R. Rao, “n-Tupled coincidence and common fixed point results for weakly contractive mappings in compatible metric spaces,” Bulletin of Mathematical Analysis and Applications, vol. 5, no. 4, pp. 19–39, 2013. View at Google Scholar