About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 359054, 14 pages
http://dx.doi.org/10.1155/2012/359054
Research Article

Theorems for Boyd-Wong-Type Contractions in Ordered Metric Spaces

1Institut Supérieur D'Informatique et des Technologies de Communication de Hammam Sousse, Université de Sousse, Route GP1-4011, Hammam Sousse, Tunisia
2Department of Mathematics, The Hashemite University, P.O. Box 13115, Zarqa 13115, Jordan
3Faculty of Applied Sciences, University Politehnica of Bucharest, 313 Splaiul Independenţei, 060042 Bucharest, Romania
4Department of Mathematics, The Hashemite University, P.O. Box 330127, Zarqa 13115, Jordan

Received 16 August 2012; Accepted 3 September 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Hassen Aydi 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. S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922.
  2. D. S. Jaggi, “Some unique fixed point theorems,” Indian Journal of Pure and Applied Mathematics, vol. 8, no. 2, pp. 223–230, 1977. View at Zentralblatt MATH
  3. 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 Zentralblatt MATH
  4. 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, vol. 23, no. 12, pp. 2205–2212, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan, “Generalized contractions in partially ordered metric spaces,” Applicable Analysis, vol. 87, no. 1, pp. 109–116, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. Amini-Harandi and H. Emami, “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 5, pp. 2238–2242, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. 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
  8. H. Aydi, “Coincidence and common fixed point results for contraction type maps in partially ordered metric spaces,” International Journal of Mathematical Analysis, vol. 5, no. 13, pp. 631–642, 2011. View at Zentralblatt MATH
  9. H. Aydi, “Some fixed point results in ordered partial metric spaces,” Journal of Nonlinear Science and its Applications, vol. 4, no. 3, pp. 210–217, 2011.
  10. H. Aydi, “Fixed point results for weakly contractive mappings in ordered partial metric spaces,” Journal of Advanced Mathematical Studies, vol. 4, no. 2, pp. 1–12, 2011. View at Zentralblatt MATH
  11. H. Aydi, “Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces,” Journal of Nonlinear Analysis and Optimization: Theory and Applications, vol. 2, no. 2, pp. 33–48, 2011.
  12. H. Aydi, “Common fixed point results for mappings satisfying (Ψ, ϕ)-weak contractions in ordered partial metric spaces,” International JMathematics and Statistics, vol. 12, no. 2, pp. 53–64, 2012.
  13. 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. Theory, Methods & Applications, vol. 74, no. 17, pp. 6814–6825, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. L. Gholizadeh, R. Saadati, W. Shatanawi, and S. M. Vaezpour, “Contractive mapping in generalized, ordered metric spaces with application in integral equations,” Mathematical Problems in Engineering, vol. 2011, Article ID 380784, 14 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. T. Gnana 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 Zentralblatt MATH
  16. J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 7-8, pp. 3403–3410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. Harjani, B. López, and K. Sadarangani, “A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space,” Abstract and Applied Analysis, vol. 2010, Article ID 190701, 8 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. E. Karapinar, “Weak φ-contraction on partial metric spaces and existence of fixed points in partially ordered sets,” Mathematica \AE terna, vol. 1, no. 3-4, pp. 237–244, 2011.
  19. 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
  20. N. V. Luong, N. X. Thuan, and T. T. THai, “Coupled fixed point theorems in partially ordered metric spaces,” Bulletin of Mathematical Analysis and Applications, vol. 3, no. 3, pp. 129–140, 2011.
  21. N. V. Luong and N. X. Thuan, “Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 46, 2011.
  22. S. Moradi and M. Omid, “A fixed-point theorem for integral type inequality depending on another function,” International Journal of Mathematical Analysis, vol. 4, no. 29-32, pp. 1491–1499, 2010. View at Zentralblatt MATH
  23. J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” A Journal on the Theory of Ordered Sets and its Applications, vol. 22, no. 3, p. 223–239, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. D. O'Regan and A. Petruşel, “Fixed point theorems for generalized contractions in ordered metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 1241–1252, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. A. Petruşel and I. A. Rus, “Fixed point theorems in ordered L-spaces,” Proceedings of the American Mathematical Society, vol. 134, no. 2, pp. 411–418, 2006. View at Publisher · View at Google Scholar
  26. W. Shatanawi, Z. Mustafa, and N. Tahat, “Some coincidence point theorems for nonlinear contraction in ordered metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 68, 2011.
  27. 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
  28. W. Shatanawi and B. Samet, “Coupled fixed point theorems for mixed monotone mappings in ordered ordered partial metric spaces,” Mathematical and Computer Modelling. In press.
  29. 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
  30. K. P. Chi, “On a fixed point theorem for certain class of maps satisfying a contractive condition depended on an another function,” Lobachevskii Journal of Mathematics, vol. 30, no. 4, pp. 289–291, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  31. D. W. Boyd and J. S. W. Wong, “On nonlinear contractions,” Proceedings of the American Mathematical Society, vol. 20, pp. 458–464, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  32. J. Jachymski, “Equivalent conditions for generalized contractions on (ordered) metric spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 3, pp. 768–774, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH