Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 134712, 13 pages
http://dx.doi.org/10.1155/2013/134712
Research Article

A Unique Coupled Common Fixed Point Theorem for Symmetric -Contractive Mappings in Ordered -Metric Spaces with Applications

1Department of Mathematics, Ahir College, Rewari 123401, India
2Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey

Received 21 July 2013; Accepted 19 October 2013

Academic Editor: Antonio J. M. Ferreira

Copyright © 2013 Manish Jain and Kenan Taş. 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 Google Scholar · View at MathSciNet
  2. 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, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. Z. Mustafa, W. Shatanawi, and M. Bataineh, “Fixed point theorems on uncomplete G-metric spaces,” Journal of Mathematics and Statistics, vol. 4, no. 4, pp. 196–201, 2008. View at Google Scholar
  4. 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 Scopus
  5. 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, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. 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 Scopus
  7. 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 · View at Scopus
  8. 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, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. 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 Scopus
  10. 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 Scopus
  11. T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods and Applications, vol. 65, no. 7, pp. 1379–1393, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. V. Lakshmikantham and L. Ćirić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods and Applications, vol. 70, no. 12, pp. 4341–4349, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. B. S. Choudhury and A. Kundu, “A coupled coincidence point result in partially ordered metric spaces for compatible mappings,” Nonlinear Analysis: Theory, Methods and Applications, vol. 73, no. 8, pp. 2524–2531, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. J. Harjani, B. Lpez, and K. Sadarangani, “Fixed point theorems for mixed monotone operators and applications to integral equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 5, pp. 1749–1760, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. N. V. Luong and N. X. Thuan, “Coupled fixed points in partially ordered metric spaces and application,” Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 3, pp. 983–992, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Samet, “Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods and Applications, vol. 72, no. 12, pp. 4508–4517, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. 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 Scopus
  18. 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 Scopus
  19. 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, English Series, vol. 23, no. 12, pp. 2205–2212, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. L. Ćirić, N. Cakić, M. Rajović, and J. S. Ume, “Monotone generalized nonlinear contractions in partially ordered metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 131294, 11 pages, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, no. 7-8, pp. 3403–3410, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Harjani and K. Sadarangani, “Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 72, no. 3-4, pp. 1188–1197, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. E. Karapinar, “Couple fixed point theorems for nonlinear contractions in cone metric spaces,” Computers and Mathematics with Applications, vol. 59, no. 12, pp. 3656–3668, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Aydi, E. Karapınar, and W. Shatanawi, “Tripled coincidence point results for generalized contractions in ordered generalized metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 101, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  25. M. Jain, K. Tas, S. Kumar, and N. Gupta, “Coupled common fixed points involving a (ϕ,ψ)—contractive condition for mixed g-monotone operators in partially ordered metric spaces,” Journal of Inequalities and Applications, vol. 2012, article 285, 2012. View at Google Scholar
  26. M. Abbas, A. R. Khan, and T. Nazir, “Coupled common fixed point results in two generalized metric spaces,” Applied Mathematics and Computation, vol. 217, no. 13, pp. 6328–6336, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. H. Aydi, B. Damjanović Bosko, B. Samet, and W. Shatanawi, “Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2443–2450, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. W. Shatanawi, M. Abbas, and B. Samet, “Common coupled fixed points for mapping satisfying (ψ,ϕ)-weakly contractive condition in generalized metric spaces,” submitted for publication. In press.
  29. N. V. Luong and N. X. Thuan, “Coupled fixed point theorems in partially ordered G-metric spaces,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 1601–1609, 2012. View at Publisher · View at Google Scholar · View at Scopus
  30. H. Aydi, M. Postolache, and W. Shatanawi, “Coupled fixed point results for (ψ, φ)-weakly contractive mappings in ordered G-metric spaces,” Computers and Mathematics with Applications, vol. 63, no. 1, pp. 298–309, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. H. K. Nashine, “Coupled common fixed point results in ordered G-metric spaces,” Journal of Nonlinear Science and Its Applications, vol. 5, no. 1, pp. 1–13, 2012. View at Google Scholar · View at MathSciNet
  32. E. Karapinar, B. Kaymakcalan, and K. Tas, “On coupled fixed point theorems on partially ordered G-metric spaces,” Journal of Inequalities and Applications, vol. 2012, article 200, 2012. View at Google Scholar
  33. S. A. Mohiuddine and A. Alotaibi, “On coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 897198, 15 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  34. H. S. Ding and E. Karapinar, “A note on some coupled fixed-point theorems on G-metric spaces,” Journal of Inequalities and Applications, vol. 2012, article 170, 2012. View at Google Scholar
  35. N. V. Luong and N. X. Thuan, “Coupled fixed points in partially ordered metric spaces and application,” Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 3, pp. 983–992, 2011. View at Publisher · View at Google Scholar · View at Scopus