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Abstract and Applied Analysis
Volume 2014, Article ID 458098, 5 pages
http://dx.doi.org/10.1155/2014/458098
Research Article

Generalized Metric Spaces Do Not Have the Compatible Topology

1Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Received 12 May 2014; Accepted 9 July 2014; Published 4 August 2014

Academic Editor: Wei-Shih Du

Copyright © 2014 Tomonari Suzuki. 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. A. Branciari, “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,” Publicationes Mathematicae Debrecen, vol. 57, no. 1-2, pp. 31–37, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. K. Włodarczyk and R. Plebaniak, “Leader type contractions, periodic and fixed points and new completivity in quasi-gauge spaces with generalized quasi-pseudodistances,” Topology and its Applications, vol. 159, no. 16, pp. 3504–3512, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. K. Włodarczyk and R. Plebaniak, “Contractions of Banach, Tarafdar, Meir-Keeler, Ćirić-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances,” Journal of Mathematical Analysis and Applications, vol. 404, no. 2, pp. 338–350, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. S. Willard, General Topology, Dover Publications, New York, NY, USA, 2004. View at MathSciNet
  5. L. Ćirić, “A new fixed-point theorem for contractive mappings,” Publications de l'Institut Mathématique, vol. 30, pp. 25–27, 1981. View at Google Scholar · View at MathSciNet
  6. J. Jachymski, “Equivalent conditions and the Meir-Keeler type theorems,” Journal of Mathematical Analysis and Applications, vol. 194, no. 1, pp. 293–303, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations, vol. 32 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. Matkowski, “Fixed point theorems for contractive mappings in metric spaces,” Časopis Pro Pěstování Matematiky, vol. 105, no. 4, pp. 341–344, 1980. View at Google Scholar · View at MathSciNet
  9. A. Fora, A. Bellour, and A. Al-Bsoul, “Some results in fixed point theory concerning generalized metric spaces,” Matematichki Vesnik, vol. 61, no. 3, pp. 203–208, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922. View at Google Scholar
  11. R. Caccioppoli, “Un teorema generale sull'esistenza di elementi uniti in una transformazione funzionale,” Rendiconti dell'Accademia Nazionale dei Lincei, vol. 11, pp. 794–799, 1930. View at Google Scholar
  12. I. R. Sarma, J. M. Rao, and S. S. Rao, “Contractions over generalized metric spaces,” Journal of Nonlinear Science and its Applications, vol. 2, no. 3, pp. 180–182, 2009. View at Google Scholar · View at MathSciNet
  13. B. Samet, “Discussion on “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces” by A. Branciari,” Publicationes Mathematicae Debrecen, vol. 76, no. 3-4, pp. 493–494, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  14. H. Lakzian and B. Samet, “Fixed points for (ψ,ϕ)-weakly contractive mappings in generalized metric spaces,” Applied Mathematics Letters, vol. 25, no. 5, pp. 902–906, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. P. N. Dutta and B. S. Choudhury, “A generalisation of contraction principle in metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 406368, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  16. T. Suzuki, “Meir-KEEler contractions of integral type are still Meir-KEEler contractions,” International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 39281, 6 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. T. Suzuki and C. Vetro, “Three existence theorems for weak contractions of Matkowski type,” International Journal of Mathematics and Statistics, vol. 6, no. 10, pp. S110–S120, 2010. View at Publisher · View at Google Scholar · View at MathSciNet