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Abstract and Applied Analysis
Volume 2014, Article ID 238191, 10 pages
http://dx.doi.org/10.1155/2014/238191
Research Article

Class 𝔄- , General Type Theorems, and Their Applications in Topological Vector Space

1School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
2College of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China

Received 12 December 2013; Accepted 14 April 2014; Published 6 May 2014

Academic Editor: Fu-quan Xia

Copyright © 2014 Gusheng Tang and Qingbang Zhang. 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. K. Fan, “A generalization of Tychonoff's fixed point theorem,” Mathematische Annalen, vol. 142, no. 3, pp. 305–310, 1961. View at Google Scholar · View at MathSciNet
  2. S. Park, “Generalizations of Ky Fan's matching theorems and their applications,” Journal of Mathematical Analysis and Applications, vol. 141, no. 1, pp. 164–176, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S.-S. Chang and Y. Zhang, “Generalized KKM theorem and variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 159, no. 1, pp. 208–223, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L.-J. Lin and T.-H. Chang, “S-KKM theorems, saddle points and minimax inequalities,” Nonlinear Analysis. Theory, Methods & Applications, vol. 34, no. 1, pp. 73–86, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. T.-H. Chang, Y.-Y. Huang, J.-C. Jeng, and K.-H. Kuo, “On S-KKM property and related topics,” Journal of Mathematical Analysis and Applications, vol. 229, no. 1, pp. 212–227, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Balaj, “Weakly G-KKM mappings, G-KKM property, and minimax inequalities,” Journal of Mathematical Analysis and Applications, vol. 294, no. 1, pp. 237–245, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Y. J. Piao, “Class W-KKM(X,Y,Z), almost fixed point theorems and fixed point theorems,” Journal of Systems Science and Mathematical Sciences, vol. 30, no. 5, pp. 665–671, 2010 (Chinese). View at Google Scholar · View at MathSciNet
  8. X. P. Ding, “Generalized L-KKM type theorems in L-convex spaces with applications,” Computers & Mathematics with Applications, vol. 43, no. 10-11, pp. 1249–1256, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C.-Y. Jin and C.-Z. Cheng, “S-G-L-KKM theorems in L-convex space and their applications to minimax inequalities,” Computers & Mathematics with Applications, vol. 50, no. 1-2, pp. 123–131, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. 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 · View at MathSciNet
  11. R. U. Verma, “Some results on R-KKM mappings and R-KKM selections and their applications,” Journal of Mathematical Analysis and Applications, vol. 232, no. 2, pp. 428–433, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X. P. Ding, “Coincidence theorems in topological spaces and their applications,” Applied Mathematics Letters, vol. 12, no. 7, pp. 99–105, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. 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 · View at MathSciNet
  14. 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 · View at MathSciNet
  15. K. Fan, “Some properties of convex sets related to fixed point theorems,” Mathematische Annalen, vol. 266, no. 4, pp. 519–537, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. F. E. Browder, “The fixed point theory of multi-valued mappings in topological vector spaces,” Mathematische Annalen, vol. 177, pp. 283–301, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. L.-J. Lin and Z.-T. Yu, “On some equilibrium problems for multimaps,” Journal of Computational and Applied Mathematics, vol. 129, no. 1-2, pp. 171–183, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. L.-J. Lin, C.-S. Chuang, and Z.-T. Yu, “Generalized KKM theorems and common fixed point theorems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 16, pp. 5591–5599, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. P. Q. Khanh, N. H. Quan, and J.-C. Yao, “Generalized KKM-type theorems in GFC-spaces and applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 3-4, pp. 1227–1234, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. Balaj and L.-J. Lin, “Equivalent forms of a generalized KKM theorem and their applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 3, pp. 673–682, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. D. Turkoglu, M. Abuloha, and T. Abdeljawad, “KKM mappings in cone metric spaces and some fixed point theorems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 1, pp. 348–353, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet