Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 673591, 12 pages
http://dx.doi.org/10.5402/2011/673591
Research Article

Fixed Points and Existence Theorems of Maximal Elements with Applications in FC-Spaces

Department of Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610103, China

Received 16 March 2011; Accepted 16 April 2011

Academic Editors: S. Utyuzhnikov and E. Yee

Copyright © 2011 Rong-Hua He. 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. Balaj, “Coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 12, pp. 3962–3971, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. M. Balaj and L. J. Lin, “Fixed points, coincidence points and maximal elements with applications to generalized equilibrium problems and minimax theory,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 1, pp. 393–403, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano, and J. V. Llinares, “Abstract convexity and fixed points,” Journal of Mathematical Analysis and Applications, vol. 222, no. 1, pp. 138–150, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. T. H. Chang and C. L. Yen, “KKM property and fixed point theorems,” Journal of Mathematical Analysis and Applications, vol. 203, no. 1, pp. 224–235, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. C. M. Chen and T. H. Chang, “Some results for the family KKM(X,Y) and the Φ-mapping,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 92–101, 2007. View at Publisher · View at Google Scholar
  6. X. P. Ding, “Maximal element principles on generalized convex spaces and their applications,” in Set Valued Mappings with Applications in Nonlinear Analysis, vol. 4 of Series in Mathematical Analysis and Applications, pp. 149–174, Taylor & Francis, London, UK, 2002. View at Google Scholar · View at Zentralblatt MATH
  7. X. P. Ding, “Maximal element theorems in product FC-spaces and generalized games,” Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp. 29–42, 2005. View at Publisher · View at Google Scholar
  8. X. P. Ding, “System of coincidence theorems in product topological spaces and applications. II,” Applied Mathematics and Mechanics, vol. 26, no. 12, pp. 1556–1563, 2005. View at Google Scholar · View at Zentralblatt MATH
  9. L. J. Lin and W. P. Wan, “KKM type theorems and coincidence theorems with applications to the existence of equilibria,” Journal of Optimization Theory and Applications, vol. 123, no. 1, pp. 105–122, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. L.J. Lin and Q. H. Ansari, “Collective fixed points and maximal elements with applications to abstract economies,” Journal of Mathematical Analysis and Applications, vol. 296, no. 2, pp. 455–472, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. L. J. Lin and H. L. Chen, “The study of KKM theorems with applications to vector equilibrium problems with implicit vector variational inequalities problems,” Journal of Global Optimization, vol. 32, no. 1, pp. 135–157, 2005. View at Publisher · View at Google Scholar
  12. M. Balaj, “Coincidence and maximal element theorems in generalized convex spaces,” Nonlinear Analysis Forum, vol. 7, no. 1, pp. 123–130, 2002. View at Google Scholar · View at Zentralblatt MATH
  13. H. Kim and S. Park, “Remarks on the KKM property for open-valued multimaps on generalized convex spaces,” Journal of the Korean Mathematical Society, vol. 42, no. 1, pp. 101–110, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Z.-T. Yu and L. J. Lin, “Continuous selection and fixed point theorems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 52, no. 2, pp. 445–455, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. X. P. Ding and T. M. Ding, “KKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces,” Journal of Mathematical Analysis and Applications, vol. 331, no. 2, pp. 1230–1245, 2007. View at Publisher · View at Google Scholar
  16. K. Fan, “Sur un théorème minimax,” Comptes Rendus de l'Académie des Sciences. Série I, vol. 259, pp. 3925–3928, 1964. View at Google Scholar · View at Zentralblatt MATH
  17. F. C. Liu, “A note on the von Neumann-Sion minimax principle,” Bulletin of the Institute of Mathematics: Academia Sinica, vol. 6, no. 2, pp. 517–524, 1978. View at Google Scholar · View at Zentralblatt MATH