Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for Journal of Applied Mathematics, enter your email address in the box below.

Journal of Applied Mathematics
Volume 2012, Article ID 312078, 15 pages
http://dx.doi.org/10.1155/2012/312078
Research Article

Coupled Coincidence Points in Partially Ordered Cone Metric Spaces with a c-Distance

Wasfi Shatanawi,1 Erdal Karapınar,2 and Hassen Aydi3

1Department of Mathematics, The Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan
2Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey
3Institut Supérieur d'Informatique et des Technologies de Communication De Hammam Sousse, Université de Sousse, Route GP1, 4011 Hammam Sousse, Tunisia

Received 22 May 2012; Revised 25 June 2012; Accepted 25 June 2012

Academic Editor: Alexander Timokha

Copyright © 2012 Wasfi Shatanawi 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. A. Yantir and S. G. Topal, “Positive solutions of nonlinear m-point BVP on time scales,” International Journal of Difference Equations, vol. 3, no. 1, pp. 179–194, 2008. View at Google Scholar
  2. Y. Guo, “A generalization of Banachs contraction principle for some non-obviously contractive operators in a cone metric space,” Turkish Journal of Mathematics, vol. 36, pp. 297–304, 2012. View at Google Scholar
  3. A. Cataldo, E. A. Lee, X. Liu, E. D. Matsikoudis, and H. Zheng, “A constructive fixed point theorem and the feedback semantics of timed systems,” Tech. Rep. UCB/EECS-2006-4, EECS Department, University of California, Berkeley, Calif, USA, 2006. View at Google Scholar
  4. A. Noumsi, S. Derrien, and P. Quinton, “Acceleration of a content based image retrieval application on the RDISK cluster,” in Proceedings of the IEEE International Parallel and Distributed Processing Symposium, April 2006.
  5. A. Hyväarinen, “Fast and robust fixed-point algorithms for independent component analysis,” IEEE Transactions on Neural Networks, vol. 10, no. 3, pp. 626–634, 1999. View at Google Scholar
  6. D. P. Mandic, J. A. Chambers, and M. M. Bozic, “On global asymptotic stability of fully connected recurrent neural networks,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP '00), vol. 6, pp. 3406–3409, 2000.
  7. K. C. Border, Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, New York, NY, USA, 1985. View at Publisher · View at Google Scholar
  8. M. H. Escardó, “PCF extended with real numbers,” Theoretical Computer Science, vol. 162, no. 1, pp. 79–115, 1996. View at Publisher · View at Google Scholar
  9. J. B. Gillespie and C. J. Houghton, “A metric space approach to the information channel capacity of spike trains,” Journal of Computational Neuroscience, vol. 30, no. 1, pp. 201–209, 2011. View at Publisher · View at Google Scholar
  10. K. Menger, “Statistical metrics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 28, pp. 535–537, 1942. View at Google Scholar
  11. D. H. Fenwick and R. P. Batycky, “Using metric space methods to analyse reservoir uncertainty,” in Proceedings of the Gussow Conference, Alberta, Canada, 2011.
  12. L. G. Huang and X. Zhang, “Cone metric spaces and fixed point theorems of contractive mappings,” Journal of Mathematical Analysis and Applications, vol. 332, no. 2, pp. 1468–1476, 2007. View at Publisher · View at Google Scholar
  13. A. Amini-Harandi and M. Fakhar, “Fixed point theory in cone metric spaces obtained via the scalarization method,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3529–3534, 2010. View at Publisher · View at Google Scholar
  14. D. Turkoglu and M. Abuloha, “Cone metric spaces and fixed point theorems in diametrically contractive mappings,” Acta Mathematica Sinica, vol. 26, no. 3, pp. 489–496, 2010. View at Publisher · View at Google Scholar
  15. H. Aydi, H. K. Nashine, B. Samet, and H. Yazidi, “Coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations,” Nonlinear Analysis, vol. 74, no. 17, pp. 6814–6825, 2011. View at Publisher · View at Google Scholar
  16. E. Graily, S. M. Vaezpour, R. Saadati, and Y. J. Cho, “Generalization of fixed point theorems in ordered metric spaces concerning generalized distance,” Fixed Point Theory and Applications, vol. 2011, article 30, 2011. View at Google Scholar
  17. S. Janković, Z. Kadelburg, and S. Radenović, “On cone metric spaces: a survey,” Nonlinear Analysis, vol. 74, no. 7, pp. 2591–2601, 2011. View at Publisher · View at Google Scholar
  18. Z. Kadelburg, M. Pavlović, and S. Radenović, “Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces,” Computers & Mathematics with Applications, vol. 59, no. 9, pp. 3148–3159, 2010. View at Publisher · View at Google Scholar
  19. Z. Kadelburg, P. P. Murthy, and S. Radenović, “Common fixed points for expansive mappings in cone metric spaces,” International Journal of Mathematical Analysis, vol. 5, no. 25–28, pp. 1309–1319, 2011. View at Google Scholar
  20. W. Sintunavarat, Y. J. Cho, and P. Kumam, “Common fixed point theorems for c-distance in ordered cone metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1969–1978, 2011. View at Publisher · View at Google Scholar
  21. W. Shatanawi and F. Awawdeh, “Some fixed and coincidence point theorems for expansive maps in cone metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 19, 2012. View at Google Scholar
  22. W. Shatanawi, “On w-compatible mappings and common coupled coincidence point in cone metric spaces,” Applied Mathematics Letters, vol. 25, pp. 925–931, 2012. View at Google Scholar
  23. W. Shatanawi, “Some coincidence point results in cone metric spaces,” Mathematical and Computer Modelling, vol. 55, pp. 2023–2028, 2012. View at Google Scholar
  24. D. Turkoglu, M. Abuloha, and T. Abdeljawad, “KKM mappings in cone metric spaces and some fixed point theorems,” Nonlinear Analysis, vol. 72, no. 1, pp. 348–353, 2010. View at Publisher · View at Google Scholar
  25. T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis, vol. 65, no. 7, pp. 1379–1393, 2006. View at Publisher · View at Google Scholar
  26. V. Lakshmikantham and L. Ćirić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Nonlinear Analysis, vol. 70, no. 12, pp. 4341–4349, 2009. View at Publisher · View at Google Scholar
  27. W. Shatanawi, “Some common coupled fixed point results in cone metric spaces,” International Journal of Mathematical Analysis, vol. 4, no. 45–48, pp. 2381–2388, 2010. View at Google Scholar
  28. H. Aydi, M. Abbas, and M. Postolache, “Coupled coincidence points for hybrid pair of mappings via mixed monotone property,” Journal of Advanced Mathematical Studies, vol. 5, no. 1, pp. 118–126, 2012. View at Google Scholar
  29. Y. J. Cho, G. He, and N. J. Huang, “The existence results of coupled quasi-solutions for a class of operator equations,” Bulletin of the Korean Mathematical Society, vol. 47, no. 3, pp. 455–465, 2010. View at Publisher · View at Google Scholar
  30. Y. J. Cho, M. H. Shah, and N. Hussain, “Coupled fixed points of weakly F-contractive mappings in topological spaces,” Applied Mathematics Letters, vol. 24, no. 7, pp. 1185–1190, 2011. View at Publisher · View at Google Scholar
  31. M. E. Gordji, Y. J. Cho, and H. Baghani, “Coupled fixed point theorems for contractions in intuitionistic fuzzy normed spaces,” Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 1897–1906, 2011. View at Publisher · View at Google Scholar
  32. E. Karapınar, “Couple fixed point theorems for nonlinear contractions in cone metric spaces,” Computers & Mathematics with Applications, vol. 59, no. 12, pp. 3656–3668, 2010. View at Publisher · View at Google Scholar
  33. W. Sintunavarat, Y. J. Cho, and P. Kumam, “Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces,” Fixed Point Theory and Applications, vol. 2011, article 81, 2011. View at Publisher · View at Google Scholar
  34. W. Shatanawi, “Partially ordered cone metric spaces and coupled fixed point results,” Computers & Mathematics with Applications, vol. 60, no. 8, pp. 2508–2515, 2010. View at Publisher · View at Google Scholar
  35. Y. J. Cho, R. Saadati, and S. Wang, “Common fixed point theorems on generalized distance in ordered cone metric spaces,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 1254–1260, 2011. View at Publisher · View at Google Scholar
  36. O. Kada, T. Suzuki, and W. Takahashi, “Nonconvex minimization theorems and fixed point theorems in complete metric spaces,” Mathematica Japonica, vol. 44, no. 2, pp. 381–391, 1996. View at Google Scholar
  37. L. Cirić, H. Lakzian, and V. Rakočević, “Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 3, 2012. View at Publisher · View at Google Scholar
  38. Z. Kadelburg and S. Radenovic, “Coupled fxed point results under tvs-cone metric and w-cone distance,” Advances in Fixed Point Theory, vol. 2, no. 1, pp. 29–46, 2012. View at Google Scholar
  39. Y. J. Cho, Z. Kadelburg, R. Saadati, and W. Shatanawi, “Coupled fixed point theorems under weak contractions,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 184534, 9 pages, 2012. View at Publisher · View at Google Scholar
  40. M. Dornevic, D. Doric, Z. Kadelburg, S. Radenovic, and D. Spaic, “Fixed point results under c-distance in tvs-cone metric spaces,” Fixed Point Theory and Its Applications, vol. 2011, article 29, 2011. View at Google Scholar