Abstract and Applied Analysis

Class 𝔄-KKM(X,Y,Z), General KKM Type Theorems, and Their Applications in Topological Vector Space

Gusheng Tang and Qingbang Zhang

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Abstract

The class 𝔄-KKM(X,Y,Z) and generalized KKM mapping are introduced, and some generalized KKM theorems are proved. As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 238191, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606937

Digital Object Identifier
doi:10.1155/2014/238191

Mathematical Reviews number (MathSciNet)
MR3208521

Citation

Tang, Gusheng; Zhang, Qingbang. Class 𝔄 - $KKM(X,Y,Z)$ , General $KKM$ Type Theorems, and Their Applications in Topological Vector Space. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 238191, 10 pages. doi:10.1155/2014/238191. https://projecteuclid.org/euclid.aaa/1412606937


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References

  • K. Fan, “A generalization of Tychonoff's fixed point theorem,” Mathematische Annalen, vol. 142, no. 3, pp. 305–310, 1961.
  • 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.
  • S.-S. Chang and Y. Zhang, “Generalized KKM theorem and var-iational inequalities,” Journal of Mathematical Analysis and App-lications, vol. 159, no. 1, pp. 208–223, 1991.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • C.-Y. Jin and C.-Z. Cheng, “S-G-L-KKM theorems in \emphL-convex space and their applications to minimax inequalities,” Computers & Mathematics with Applications, vol. 50, no. 1-2, pp. 123–131, 2005.
  • 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.
  • R. U. Verma, “Some results on R-KKM mappings and R-KKM selections and their applications,” Journal of Mathematical Ana-lysis and Applications, vol. 232, no. 2, pp. 428–433, 1999.
  • X. P. Ding, “Coincidence theorems in topological spaces and their applications,” Applied Mathematics Letters, vol. 12, no. 7, pp. 99–105, 1999.
  • 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.
  • 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.
  • K. Fan, “Some properties of convex sets related to fixed point theorems,” Mathematische Annalen, vol. 266, no. 4, pp. 519–537, 1984.
  • F. E. Browder, “The fixed point theory of multi-valued mappings in topological vector spaces,” Mathematische Annalen, vol. 177, pp. 283–301, 1968.
  • 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.
  • L.-J. Lin, C.-S. Chuang, and Z.-T. Yu, “Generalized KKM theor-ems and common fixed point theorems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 16, pp. 5591–5599, 2011.
  • 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.
  • 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.
  • 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. \endinput