Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 126205, 11 pages
http://dx.doi.org/10.1155/2011/126205
Research Article

Some Fixed Point Theorems in Ordered 𝐺-Metric Spaces and Applications

Department of Mathematics, The Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan

Received 9 January 2011; Revised 22 March 2011; Accepted 19 April 2011

Academic Editor: D. Anderson

Copyright © 2011 W. Shatanawi. 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. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435–1443, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan, “Generalized contractions in partially ordered metric spaces,” Applicable Analysis, vol. 87, no. 1, pp. 109–116, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. J. J. Nieto and R. Rodríguez-López, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations,” Acta Mathematica Sinica, vol. 23, no. 12, pp. 2205–2212, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. J. Nieto, R. L. Pouso, and R. Rodríguez-López, “Fixed point theorems in ordered abstract spaces,” Proceedings of the American Mathematical Society, vol. 135, no. 8, pp. 2505–2517, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. D. O'Regan and A. Petruşel, “Fixed point theorems for generalized contractions in ordered metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 2505–2517, 2007. View at Publisher · View at Google Scholar
  7. 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 Zentralblatt MATH
  8. Z. Mustafa and B. Sims, “Some remarks concerning D-metric spaces,” in Proceedings of the International Conference on Fixed Point Theory and Applications, pp. 189–198, Valencia, Spain, July 2003.
  9. Z. Mustafa, W. Shatanawi, and M. Bataineh, “Existence of fixed point results in G-metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 283028, 10 pages, 2009. View at Publisher · View at Google Scholar
  10. Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 189870, 12 pages, 2008. View at Publisher · View at Google Scholar
  11. M. Abbas and B. E. Rhoades, “Common fixed point results for noncommuting mappings without continuity in generalized metric spaces,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 262–269, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. R. Chugh, T. Kadian, A. Rani, and B. E. Rhoades, “Property p in G-metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 401684, 12 pages, 2010. View at Publisher · View at Google Scholar
  13. R. Saadati, S. M. Vaezpour, P. Vetro, and B. E. Rhoades, “Fixed point theorems in generalized partially ordered G-metric spaces,” Mathematical and Computer Modelling, vol. 52, no. 5-6, pp. 797–801, 2010. View at Publisher · View at Google Scholar
  14. W. Shatanawi, “Fixed point theory for contractive mappings satisfying Φ-maps in Gmetric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 181650, 9 pages, 2010. View at Publisher · View at Google Scholar
  15. H. Aydi, B. Damjanović, B. Samet, and W. Shatanawi, “Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces,” Mathematical and Computer Modelling. In press. View at Publisher · View at Google Scholar
  16. I. Altun and H. Simsek, “Some fixed point theorems on ordered metric spaces and application,” Fixed Point Theory and Applications, vol. 2010, Article ID 621469, 17 pages, 2010. View at Google Scholar · View at Zentralblatt MATH
  17. B. Ahmed and J. J. Nieto, “The monotone iterative technique for three-point secondorder integrodifferential boundary value problems with p-Laplacian,” Boundary Value Problems, vol. 2007, Article ID 57481, 9 pages, 2007. View at Publisher · View at Google Scholar
  18. A. Cabada and J. J. Nieto, “Fixed points and approximate solutions for nonlinear operator equations,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 17–25, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. J. J. Nieto, “An abstract monotone iterative technique,” Nonlinear Analysis: Theory Method and Applications, vol. 28, no. 12, pp. 1923–1933, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH