Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2014, Article ID 269286, 10 pages
http://dx.doi.org/10.1155/2014/269286
Research Article

A Proposal to the Study of Contractions in Quasi-Metric Spaces

1Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
3Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran
4Department of Mathematics, University of Jaén, Campus las Lagunillas s/n, 23071 Jaén, Spain

Received 28 March 2014; Accepted 10 July 2014; Published 6 August 2014

Academic Editor: Janusz Brzdęk

Copyright © 2014 Hamed H. Alsulami et al. 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. M. Jleli and B. Samet, “Remarks on G-metric spaces and fixed point theorems,” Fixed Point Theory and Applications, vol. 2012, article 210, 2012. View at Publisher · View at Google Scholar
  2. B. Samet, C. Vetro, and F. Vetro, “Remarks on G-metric spaces,” International Journal of Analysis, vol. 2013, Article ID 917158, 6 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  3. Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, pp. 289–297, 2006. View at Google Scholar · View at MathSciNet
  4. F. Khojasteh, S. Shukla, and S. Radenović, “A new approach to the study of fixed point theorems via simulation functions,” Filomat. In press.
  5. M. S. 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 · View at MathSciNet
  6. F. E. Browder and W. V. Petryshyn, “The solution by iteration of nonlinear functional equations in Banach spaces,” Bulletin of the American Mathematical Society, vol. 72, pp. 571–575, 1966. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Banach, “Sur les opérations dans les ensembles abstraits et leur application auxéquations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922. View at Google Scholar
  8. B. E. Rhoades, “Some theorems on weakly contractive maps,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, pp. 2683–2693, 2001. View at Google Scholar
  9. D. W. Boyd and J. S. W. Wong, “On nonlinear contractions,” Proceedings of the American Mathematical Society, vol. 20, no. 2, pp. 458–464, 1969. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Z. Mustafa and B. Sims, “Fixed point theorems for contractive mappings in complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 917175, 10 pages, 2009. View at Google Scholar · View at MathSciNet
  11. Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory [Ph.D. thesis], The University of Newcastle, Callaghan, Australia, 2005.
  12. R. Agarwal, E. Karapınar, and A. F. Roldán-López-de-Hierro, “Fixed point theorems in quasi-metric spaces and applications to coupled/tripled fixed points on G*-metric spaces,” Journal of Nonlinear and Convex Analysis. In press.
  13. C. T. Aage and J. N. Salunke, “Fixed points for weak contractions in G-metric spaces,” Applied Mathematics E-Notes, vol. 12, pp. 23–28, 2012. View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. P. Agarwal and E. Karapınar, “Remarks on some coupled fixed point theorems in G-metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 2, 33 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. W. Shatanawi, “Fixed point theory for contractive mappings satisfying ϕ-maps in G-metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 181650, 9 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet