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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 701910, 18 pages
http://dx.doi.org/10.1155/2012/701910
Research Article

On Generalized Weakly -Contractive Mappings in Partially Ordered -Metric Spaces

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Received 3 August 2012; Accepted 6 September 2012

Academic Editor: Naseer Shahzad

Copyright © 2012 A. Razani and V. Parvaneh. 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. 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 Zentralblatt MATH
  2. M. Abbas, T. Nazir, and D. Dorić, “Common fixed point of mappings satisfying (E,A) property in generalized metric spaces,” Applied Mathematics and Computation, vol. 218, no. 14, pp. 7665–7670, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. M. Abbas, T. Nazir, and S. Radenović, “Common fixed point of generalized weakly contractive maps in partially ordered G-metric spaces,” Applied Mathematics and Computation, vol. 218, no. 18, pp. 9383–9395, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. Abbas, T. Nazir, and S. Radenović, “Some periodic point results in generalized metric spaces,” Applied Mathematics and Computation, vol. 217, no. 8, pp. 4094–4099, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. H. Aydi, W. Shatanawi, and C. Vetro, “On generalized weak G-contraction mapping in G-metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 11, pp. 4223–4229, 2011. View at Publisher · View at Google Scholar
  6. M. Khandaqji, Sh. Al-Sharif, and M. Al-Khaleel, “Properpty P and some fixed point results on (ψ,φ)-weakly contractive G-metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 675094, 11 pages, 2012. View at Publisher · View at Google Scholar
  7. Z. Mustafa, M. Khandagji, and W. Shatanawi, “Fixed point results on complete G-metric spaces,” Studia Scientiarum Mathematicarum Hungarica, vol. 48, no. 3, pp. 304–319, 2011. View at Publisher · View at Google Scholar
  8. Z. Mustafa and H. Obiedat, “A fixed point theorem of Reich in G-metric spaces,” CUBO: A Mathematical Journal, vol. 12, no. 1, pp. 83–93, 2010. View at Zentralblatt MATH
  9. 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 Zentralblatt MATH
  10. 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 · View at Zentralblatt MATH
  11. 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 Zentralblatt MATH
  12. 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
  13. W. Shatanawi, “Some fixed point theorems in ordered G-metric spaces and applications,” Abstract and Applied Analysis, vol. 2011, Article ID 126205, 11 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. N. Tahat, H. Aydi, E. Karapınar, and W. Shatanawi, “Common fixed point for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 48, 2012. View at Publisher · View at Google Scholar
  15. B. S. Choudhury and P. Maity, “Coupled fixed point results in generalized metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 73–79, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. 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 Zentralblatt MATH
  17. B. S. Choudhury, “Unique fixed point theorem for weak C-contractive mappings,” Kathmandu University Journal of Science, Engineering and Technology, vol. 5, no. 1, pp. 6–13, 2009.
  18. J. Harjani, B. Lopez, and K. Sadarangani, “Fixed point theorems for weakly C-contractive mappings in ordered metric spaces,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 790–796, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. W. Shatanawi, “Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 2816–2826, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. M. Abbas, T. Nazir, and S. Radenović, “Common fixed points of four maps in partially ordered metric spaces,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1520–1526, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. H. K. Nashine and B. Samet, “Fixed point results for mappings satisfying (ψ,φ)-weakly contractive condition in partially ordered metric spaces,” Nonlinear Analysis, vol. 74, no. 6, pp. 2201–2209, 2011. View at Publisher · View at Google Scholar
  22. G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771–779, 1986. View at Publisher · View at Google Scholar
  23. 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 Zentralblatt MATH
  24. W. Shatanawi and B. Samet, “On (ψ,φ)-weakly contractive condition in partially ordered metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 8, pp. 3204–3214, 2011. View at Publisher · View at Google Scholar
  25. M. Kumar, “Compatible maps in G-metric spaces,” International Journal of Mathematical Analysis, vol. 6, no. 29, pp. 1415–1421, 2012.
  26. M. Abbas, V. Parvaneh, and A. Razani, “Periodic point of T-Ciric generalized contraction mappings in ordered metric spaces,” Georgian Mathematical Journal. In press.
  27. 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 Zentralblatt MATH
  28. G. S. Jeong and B. E. Rhoades, “Maps for which F(T)=F(Tn),” Fixed Point Theory and Applications, vol. 6, pp. 87–131, 2005.