About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 815289, 7 pages
http://dx.doi.org/10.1155/2013/815289
Research Article

Fixed Point and Common Fixed Point Theorems on Ordered Cone b-Metric Spaces

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia

Received 28 February 2013; Accepted 18 April 2013

Academic Editor: Abdelghani Bellouquid

Copyright © 2013 Sahar Mohammad Abusalim and Mohd Salmi Md Noorani. 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. Y. J. Cho, “Fixed points for compatible mappings of type (A),” Mathematica Japonica, vol. 18, pp. 497–508, 1993. View at Zentralblatt MATH · View at MathSciNet
  2. Y. J. Cho, H. K. Pathak, S. M. Kang, and J. S. Jung, “Common fixed points of compatible maps of type (β) on fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 93, no. 1, pp. 99–111, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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 · View at Zentralblatt MATH · View at MathSciNet
  4. G. Jungck, Y. J. Cho, and P. P. Murthy, “Compatible mappings of type (A) and common fixed points,” Mathematica Japonica, vol. 38, no. 2, pp. 381–390, 1993. View at Zentralblatt MATH · View at MathSciNet
  5. A. Kaewkhao, W. Sintunavarat, and P. Kumam, “Common fixed point theorems of c-distance on cone metric spaces,” Journal of Nonlinear Analysis and Application, vol. 2012, Article ID jnaa-00137, 11 pages, 2012. View at Publisher · View at Google Scholar
  6. J. S. Vandergraft, “Newton's method for convex operators in partially ordered spaces,” SIAM Journal on Numerical Analysis, vol. 4, pp. 406–432, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. \'Cirić, M. Abbas, R. Saadati, and N. Hussain, “Common fixed points of almost generalized contractive mappings in ordered metric spaces,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5784–5789, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. I. Altun and G. Durmaz, “Some fixed point theorems on ordered cone metric spaces,” Rendiconti del Circolo Matematico di Palermo, vol. 58, no. 2, pp. 319–325, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. I. Altun, B. Damjanović, and D. Djorić, “Fixed point and common fixed point theorems on ordered cone metric spaces,” Applied Mathematics Letters, vol. 23, no. 3, pp. 310–316, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. 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 · View at Zentralblatt MATH · View at MathSciNet
  11. B. S. Choudhury and N. Metiya, “Fixed point and common fixed point results in ordered cone metric spaces,” Analele Stiintifice ale Universitatii Ovidius Constanta, vol. 20, no. 1, pp. 55–72, 2012. View at MathSciNet
  12. 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 · View at Zentralblatt MATH · View at MathSciNet
  13. H. K. Nashine, Z. Kadelburg, and S. Radenović, “Coupled common fixed point theorems for w*-compatible mappings in ordered cone metric spaces,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5422–5432, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. R. P. Agarwal, W. Sintunavarat, and P. Kumam, “Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property,” Fixed Point Theory and Applications, vol. 2013, article 22, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. 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 · View at Zentralblatt MATH · View at MathSciNet
  16. 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 · View at MathSciNet
  17. 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 · View at Zentralblatt MATH · View at MathSciNet
  18. N. Hussain and M. H. Shah, “KKM mappings in cone b-metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1677–1684, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  19. H. Aydi, M.-F. Bota, E. Karapinar, and S. Mitrović, “A fixed point theorem for set-valued quasi-contractions in b-metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 88, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. A. S. Cvetković, M. P. Stanić, S. Dimitrijević, and S. Simić, “Common fixed point theorems for four mappings on cone metric type space,” Fixed Point Theory and Applications, vol. 2011, Article ID 589725, 15 pages, 2011. View at Zentralblatt MATH · View at MathSciNet
  21. M. P. Stanić, A. S. Cvetković, S. Simić, and S. Dimitrijević, “Common fixed point under contractive condition of Cirics type on cone metric type spaces,” Fixed Point Theory and Applications, vol. 2012, article 35, 2012. View at Publisher · View at Google Scholar
  22. M. H. Shah, S. Simić, N. Hussain, A. Sretenović, and S. Radenović, “Common fixed points theorems for occasionally weakly compatible pairs on cone metric type spaces,” Journal of Computational Analysis and Applications, vol. 14, no. 2, pp. 290–297, 2012. View at Zentralblatt MATH · View at MathSciNet
  23. H. Huang and S. Xu, “Fixed point theorems of contractive mappings in cone b-metric spaces and applications,” Fixed Point Theory and Applications, vol. 2012, article 220, 2012. View at Publisher · View at Google Scholar
  24. G. Jungck, S. Radenović, S. Radojević, and V. Rakočević, “Common fixed point theorems for weakly compatible pairs on cone metric spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 643840, 13 pages, 2009. View at Zentralblatt MATH · View at MathSciNet