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Abstract and Applied Analysis
Volume 2014, Article ID 104762, 5 pages
http://dx.doi.org/10.1155/2014/104762
Research Article

A General Fixed Point Theorem for Multivalued Mappings That Are Not Necessarily Contractions and Applications

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Avignon University, LMA-EA2151, 84000 Avignon, France

Received 13 May 2014; Accepted 5 June 2014; Published 17 June 2014

Academic Editor: Jen-Chih Yao

Copyright © 2014 Abdul Latif and Dinh The Luc. 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. R. P. Agarwal, M. Meehan, and D. O'Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, Mass, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. Balaj, “A fixed point-equilibrium theorem with applications,” Bulletin of the Belgian Mathematical Society, vol. 17, no. 5, pp. 919–928, 2010. View at Google Scholar · View at MathSciNet
  3. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  5. M. A. Khamsi and W. A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Pure and Applied Mathematics, John Wiley and Sons, New York, NY, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. B. Nadler Jr., “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475–488, 1969. View at Google Scholar · View at MathSciNet
  7. J. T. Markin, “A fixed point theorem for set valued mappings,” Bulletin of the American Mathematical Society, vol. 74, pp. 639–640, 1968. View at Google Scholar · View at MathSciNet
  8. T. H. Chang, “Common fixed point theorems for multivalued mappings,” Mathematica Japonica, vol. 41, no. 2, pp. 311–320, 1995. View at Google Scholar · View at MathSciNet
  9. L. Ćirić, “Multi-valued nonlinear contraction mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2716–2723, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. L. Ćirić, “Fixed point theorems for multi-valued contractions in complete metric spaces,” Journal of Mathematical Analysis and Applications, vol. 348, no. 1, pp. 499–507, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  11. P. Z. Daffer and H. Kaneko, “Fixed points of generalized contractive multi-valued mappings,” Journal of Mathematical Analysis and Applications, vol. 192, no. 2, pp. 655–666, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Y. Feng and S. Liu, “Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings,” Journal of Mathematical Analysis and Applications, vol. 317, no. 1, pp. 103–112, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Jachymski, “On Reich's question concerning fixed points of multimaps,” Unione Matematica Italiana: Bollettino A: Serie VII, vol. 9, no. 3, pp. 453–460, 1995. View at Google Scholar · View at MathSciNet
  14. D. Klim and D. Wardowski, “Fixed point theorems for set-valued contractions in complete metric spaces,” Journal of Mathematical Analysis and Applications, vol. 334, no. 1, pp. 132–139, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  15. A. Latif and A. A. N. Abdou, “Multivalued generalized nonlinear contractive maps and fixed points,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 4, pp. 1436–1444, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. A. Latif and D. T. Luc, “Variational relation problems: existence of solutions and fixed points of contraction mappings,” Fixed Point Theory and Applications, vol. 315, pp. 1–10, 2013. View at Google Scholar
  17. A. Latif and I. Tweddle, “Some results on coincidence points,” Bulletin of the Australian Mathematical Society, vol. 59, no. 1, pp. 111–117, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  18. N. Mizoguchi and W. Takahashi, “Fixed point theorems for multivalued mappings on complete metric spaces,” Journal of Mathematical Analysis and Applications, vol. 141, no. 1, pp. 177–188, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  19. T. Suzuki, “Mizoguchi-Takahashi's fixed point theorem is a real generalization of Nadler's,” Journal of Mathematical Analysis and Applications, vol. 340, no. 1, pp. 752–755, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  20. W.-S. Du and F. Khojasteh, “New results and generalizations for approximate fixed point property and their applications,” Abstract and Applied Analysis, vol. 2014, Article ID 581267, 9 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet