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The Scientific World Journal
Volume 2013, Article ID 194897, 8 pages
http://dx.doi.org/10.1155/2013/194897
Research Article

Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces

1Department of Mathematics, International Islamic University, H-10, Islamabad 44000, Pakistan
2Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad 44000, Pakistan

Received 30 April 2013; Accepted 18 June 2013

Academic Editors: A. Bekir, A. Ibeas, and A. M. Peralta

Copyright © 2013 Abdullah Shoaib 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. M. Abbas, M. Arshad, and A. Azam, “Fixed points of asymptotically regular mappings in complex-valued metric spaces,” Georgian Mathematical Journal, vol. 20, no. 2, pp. 213–221, 2013. View at Publisher · View at Google Scholar
  2. J. Ahmad, M. Arshad, and C. Vetro, “On a theorem of Khan in a generalized metric space,” International Journal of Analysis, vol. 2013, Article ID 852727, 6 pages, 2013. View at Publisher · View at Google Scholar
  3. M. Arshad, J. Ahmad, and E. Karapinar, “Some common fixed point results in rectangular metric spaces,” International Journal of Analysis, vol. 2013, Article ID 307234, 7 pages, 2013. View at Publisher · View at Google Scholar
  4. K. Leibovic, “The principle of contration mapping in nonlinear and adoptive controle systems,” IEEE Transactions on Automatic Control, vol. 9, pp. 393–398, 1964. View at Publisher · View at Google Scholar
  5. G. A. Medrano-Cerda, “A fixed point formulation to parameter estimation problems,” in Proceedings of the 26th IEEE Conference on Decision and Control, pp. 1468–1476, 1987.
  6. J. E. Steck, “Convergence of recurrent networks as contraction mappings,” Neural Networks, vol. 3, pp. 7–11, 1992. View at Google Scholar
  7. 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
  8. 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
  9. I. Altun and H. Simsek, “Some fixed point theorems on ordered metric spaces and application,” Fixed Point Theory and Applications, vol. 2010, Article ID 621492, 17 pages, 2010. View at Publisher · View at Google Scholar
  10. T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 7, pp. 1379–1393, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. H. K. Nashine, B. Samet, and C. Vetro, “Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 712–720, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. S. G. Matthews, “Partial metric topology,” Annals of the New York Academy of Sciences, vol. 728, pp. 183–197, 1994. View at Publisher · View at Google Scholar · View at Scopus
  13. M. A. Bukatin and S. Yu. Shorina, “Partial metrics and co-continuous valuations,” in Foundations of Software Science and Computation Structure, M. Nivat et al., Ed., vol. 1378 of Lecture Notes in Computer Science, pp. 125–139, Springer, 1998. View at Google Scholar
  14. I. Altun and A. Erduran, “Fixed point theorems for monotone mappings on partial metric spaces,” Fixed Point Theory and Applications, vol. 2011, Article ID 508730, 10 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Paesano and P. Vetro, “Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces,” Topology and Its Applications, vol. 159, no. 3, pp. 911–920, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. E. Karapınar, İ. M. Erhan, and A. Öztürk, “Fixed point theorems on quasi-partial metric spaces,” Mathematical and Computer Modelling, vol. 57, no. 9-10, pp. 2442–2448, 2013. View at Publisher · View at Google Scholar
  17. S. Romaguera, “A Kirk type characterization of completeness for partial metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 493298, 6 pages, 2010. View at Publisher · View at Google Scholar
  18. H. K. Nashine, Z. Kadelburg, S. Radenovic, and J. K. Kim, “Fixed point theorems under Hardy-Rogers contractive conditions on 0-complete ordered partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 180, 2012. View at Publisher · View at Google Scholar
  19. M. Arshad, A. Shoaib, and I. Beg, “Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space,” Fixed Point Theory and Applications, vol. 2013, article 115, 2013. View at Publisher · View at Google Scholar
  20. A. Azam, S. Hussain, and M. Arshad, “Common fixed points of Chatterjea type fuzzy mappings on closed balls,” Neural Computing and Applications, vol. 21, no. 1, supplement, pp. 313–317, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Azam, M. Waseem, and M. Rashid, “Fixed point theorems for fuzzy contractive mappings in quasi-pseudo-metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 27, 2013. View at Publisher · View at Google Scholar
  22. M. Abbas and S. Z. Németh, “Finding solutions of implicit complementarity problems by isotonicity of the metric projection,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 4, pp. 2349–2361, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. E. Kryeyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, New York, NY, USA, 1989.