Abstract and Applied Analysis

Generalized Metric Spaces Do Not Have the Compatible Topology

Tomonari Suzuki

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study generalized metric spaces, which were introduced by Branciari (2000). In particular, generalized metric spaces do not necessarily have the compatible topology. Also we prove a generalization of the Banach contraction principle in complete generalized metric spaces.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 458098, 5 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606559

Digital Object Identifier
doi:10.1155/2014/458098

Mathematical Reviews number (MathSciNet)
MR3248859

Zentralblatt MATH identifier
07022418

Citation

Suzuki, Tomonari. Generalized Metric Spaces Do Not Have the Compatible Topology. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 458098, 5 pages. doi:10.1155/2014/458098. https://projecteuclid.org/euclid.aaa/1412606559


Export citation

References

  • 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.
  • 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.
  • 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.
  • S. Willard, General Topology, Dover Publications, New York, NY, USA, 2004.
  • L. Ćirić, “A new fixed-point theorem for contractive mappings,” Publications de l'Institut Mathématique, vol. 30, pp. 25–27, 1981.
  • J. Jachymski, “Equivalent conditions and the Meir-Keeler type theorems,” Journal of Mathematical Analysis and Applications, vol. 194, no. 1, pp. 293–303, 1995.
  • 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.
  • J. Matkowski, “Fixed point theorems for contractive mappings in metric spaces,” Časopis Pro Pěstování Matematiky, vol. 105, no. 4, pp. 341–344, 1980.
  • 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.
  • S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922.
  • 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.
  • 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.
  • 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.
  • H. Lakzian and B. Samet, “Fixed points for ($\psi ,\phi $)-weakly contractive mappings in generalized metric spaces,” Applied Mathematics Letters, vol. 25, no. 5, pp. 902–906, 2012.
  • 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.
  • 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.
  • 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. \endinput