Table of Contents 
ISRN Applied Mathematics
Volume 2011, Article ID 696917, 13 pages
http://dx.doi.org/10.5402/2011/696917
Research Article

Some Results for the Family KKM(X,Y) and the ฮฆ-Mapping in FC-Spaces

Rong-Hua He

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

Received 15 July 2011; Accepted 24 August 2011

Academic Editor: A. Bellouquid

Copyright ยฉ 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. H. Knaster, C. Kuratowski, and S. Mazurkiewicz, โ€œEin Beweis des Fixpunktsatzes fรผr n-dimensional simplexe,โ€ Fundamenta Mathematicae, vol. 14, pp. 132โ€“137, 1929. View at Google Scholar
  2. K. Fan, โ€œA generalization of Tychonoff's fixed point theorem,โ€ Mathematische Annalen, vol. 142, pp. 305โ€“310, 1961. View at Google Scholar
  3. T. H. Chang and C. L. Yen, โ€œKKM property and fixed point theorems,โ€ Journal of Mathematical Analysis and Applications, vol. 203, no. 1, pp. 224โ€“235, 1996. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH
  4. L. J. Lin and H. I. Chen, โ€œCoincidence theorems for families of multimaps and their applications to equilibrium problems,โ€ Abstract and Applied Analysis, vol. 2003, no. 5, pp. 295โ€“309, 2003. View at Publisher ยท View at Google Scholar
  5. C. M. Chen and T. H. Chang, โ€œSome results for the family KKM(X, Y) and the ฮฆ-mapping,โ€ Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 92โ€“101, 2007. View at Publisher ยท View at Google Scholar
  6. A. Amini, M. Fakhar, and J. Zafarani, โ€œKKM mappings in metric spaces,โ€ Nonlinear Analysis: Theory, Methods & Applications, vol. 60, no. 6, pp. 1045โ€“1052, 2005. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH
  7. X. P. Ding, โ€œAbstract convexity and generalizations of Himmelberg type fixed-point theorems,โ€ Computers & Mathematics with Applications, vol. 41, no. 3-4, pp. 497โ€“504, 2001. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH
  8. X. P. Ding, โ€œGeneralizations of Himmelberg type fixed point theorems in locally FC-spaces,โ€ Journal of Sichuan Normal University, vol. 29, no. 1, pp. 1โ€“6, 2006. View at Google Scholar ยท View at Zentralblatt MATH
  9. X. P. Ding and T. M. Ding, โ€œKKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces,โ€ Journal of Mathematical Analysis and Applications, vol. 331, no. 2, pp. 1230โ€“1245, 2007. View at Publisher ยท View at Google Scholar
  10. J. C. Jeng, H. C. Hsu, and Y. Y. Huang, โ€œFixed point theorems for multifunctions having KKM property on almost convex sets,โ€ Journal of Mathematical Analysis and Applications, vol. 319, no. 1, pp. 187โ€“198, 2006. View at Publisher ยท View at Google Scholar ยท View at Zentralblatt MATH
  11. X. P. Ding, โ€œSystem of generalized vector quasi-equilibrium problems in locally FC-space,โ€ Acta Mathematica Sinica. In press.
  12. X. P. Ding, โ€œMaximal element theorems in product FC-spaces and generalized games,โ€ Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp. 29โ€“42, 2005. View at Publisher ยท View at Google Scholar
  13. X. P. Ding, โ€œCollective fixed points and a system of coincidence theorems in product FC-spaces and applications,โ€ Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 11, pp. 2604โ€“2617, 2007. View at Publisher ยท View at Google Scholar