Fixed Point Theory and Applications

, 2006:72184 | Cite as

Coincidence and fixed point theorems for functions in Open image in new window -KKM class on generalized convex spaces

  • Tian-Yuan Kuo
  • Young-Ye Huang
  • Jyh-Chung Jeng
  • Chen-Yuh Shih
Open Access
Research Article


We establish a coincidence theorem in Open image in new window -KKM class by means of the basic defining property for multifunctions in Open image in new window -KKM. Based on this coincidence theorem, we deduce some useful corollaries and investigate the fixed point problem on uniform spaces.


Differential Geometry Computational Biology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Browder FE: The fixed point theory of multi-valued mappings in topological vector spaces. Mathematische Annalen 1968, 177: 283–301. 10.1007/BF01350721MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Browder FE: Coincidence theorems, minimax theorems, and variational inequalities. In Conference in Modern Analysis and Probability (New Haven, Conn, 1982), Contemp. Math.. Volume 26. American Mathematical Society, Rhode Island; 1984:67–80.CrossRefGoogle Scholar
  3. 3.
    Chang T-H, Huang Y-Y, Jeng J-C, Kuo K-H: On -KKM property and related topics. Journal of Mathematical Analysis and Applications 1999,229(1):212–227. 10.1006/jmaa.1998.6154MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Chang T-H, Yen C-L: KKM property and fixed point theorems. Journal of Mathematical Analysis and Applications 1996,203(1):224–235. 10.1006/jmaa.1996.0376MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Fan K: A generalization of Tychonoff's fixed point theorem. Mathematische Annalen 1960/1961, 142: 305–310.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Granas A, Liu FC: Coincidences for set-valued maps and minimax inequalities. Journal de Mathématiques Pures et Appliquées. Neuvième Série(9) 1986,65(2):119–148.MathSciNetMATHGoogle Scholar
  7. 7.
    Horvath CD: Contractibility and generalized convexity. Journal of Mathematical Analysis and Applications 1991,156(2):341–357. 10.1016/0022-247X(91)90402-LMathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Kelley JL: General Topology. D. Van Nostrand, Toronto; 1955:xiv+298.Google Scholar
  9. 9.
    Lassonde M: On the use of KKM multifunctions in fixed point theory and related topics. Journal of Mathematical Analysis and Applications 1983,97(1):151–201. 10.1016/0022-247X(83)90244-5MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Lin L-J, Park S: On some generalized quasi-equilibrium problems. Journal of Mathematical Analysis and Applications 1998,224(2):167–181. 10.1006/jmaa.1998.5964MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Park S: Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps. Journal of the Korean Mathematical Society 1994,31(3):493–519.MathSciNetMATHGoogle Scholar
  12. 12.
    Park S, Kim H: Coincidence theorems for admissible multifunctions on generalized convex spaces. Journal of Mathematical Analysis and Applications 1996,197(1):173–187. 10.1006/jmaa.1996.0014MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Park S, Kim H: Foundations of the KKM theory on generalized convex spaces. Journal of Mathematical Analysis and Applications 1997,209(2):551–571. 10.1006/jmaa.1997.5388MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Watson PJ: Coincidences and fixed points in locally G-convex spaces. Bulletin of the Australian Mathematical Society 1999,59(2):297–304. 10.1017/S0004972700032901MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Tian-Yuan Kuo et al. 2006

This article is published under license to BioMed Central Ltd. 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.

Authors and Affiliations

  • Tian-Yuan Kuo
    • 1
  • Young-Ye Huang
    • 2
  • Jyh-Chung Jeng
    • 3
  • Chen-Yuh Shih
    • 4
  1. 1.Fooyin UniversityTa-Liao HsiangTaiwan
  2. 2.Center for General EducationSouthern Taiwan University of TechnologyYung-Kang CityTaiwan
  3. 3.Nan-Jeon Institute of TechnologyYen-ShuiTaiwan
  4. 4.Department of MathmaticsCheng Kung UniversityTainanTaiwan

Personalised recommendations