Open Access

Coincidence Theorems, Generalized Variational Inequality Theorems, and Minimax Inequality Theorems for the -Mapping on -Convex Spaces

Fixed Point Theory and Applications20072007:078696

DOI: 10.1155/2007/78696

Received: 14 December 2006

Accepted: 5 March 2007

Published: 7 May 2007


We establish some coincidence theorems, generalized variational inequality theorems, and minimax inequality theorems for the family -KKM and the -mapping on -convex spaces.


Authors’ Affiliations

Department of Applied Mathematics, National Hsinchu University of Education


  1. Knaster B, Kurnatoaski C, Mazurkiewicz S: Ein Beweis des Fixpunksatzes fur -dimensionale simplexe. Fundamenta Mathematicae 1929, 14: 132–137.MATHGoogle Scholar
  2. Fan K: A generalization of Tychonoff's fixed point theorem. Mathematische Annalen 1961, 142: 305–310. 10.1007/BF01353421MATHMathSciNetView ArticleGoogle Scholar
  3. Chang T-H, Yen C-L: property and fixed point theorems. Journal of Mathematical Analysis and Applications 1996,203(1):224–235. 10.1006/jmaa.1996.0376MATHMathSciNetView ArticleGoogle Scholar
  4. Ansari QH, Idzik A, Yao J-C: Coincidence and fixed point theorems with applications. Topological Methods in Nonlinear Analysis 2000,15(1):191–202.MATHMathSciNetGoogle Scholar
  5. Lin L-J, Chen HI: Coincidence theorems for families of multimaps and their applications to equilibrium problems. Abstract and Applied Analysis 2003,2003(5):295–309. 10.1155/S1085337503210034MATHView ArticleGoogle Scholar
  6. Ding XP: Existence of solutions for quasi-equilibrium problems in noncompact topological spaces. Computers & Mathematics with Applications 2000,39(3–4):13–21. 10.1016/S0898-1221(99)00329-6MATHView ArticleGoogle Scholar
  7. Tian GQ, Zhou J: Transfer continuities, generalizations of the Weierstrass and maximum theorems: a full characterization. Journal of Mathematical Economics 1995,24(3):281–303. 10.1016/0304-4068(94)00687-6MATHMathSciNetView ArticleGoogle Scholar
  8. 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.1996.0014MATHMathSciNetView ArticleGoogle Scholar
  9. Yuan GX-Z: KKM Theorem and Application in Nonlinear Analysis, Monographs and Textbooks in Pure and Applied Mathematics. Volume 218. Marcel Dekker, New York, NY, USA; 1999:xiv+621.Google Scholar
  10. Ding XP: Coincidence theorems in topological spaces and their applications. Applied Mathematics Letters 1999,12(7):99–105. 10.1016/S0893-9659(99)00108-1MATHMathSciNetView ArticleGoogle Scholar
  11. Lin L-J: System of coincidence theorems with applications. Journal of Mathematical Analysis and Applications 2003,285(2):408–418. 10.1016/S0022-247X(03)00406-2MATHMathSciNetView ArticleGoogle Scholar
  12. Chang T-H, Lee YL: theorem and its applications. J. Graduate Institute of Mathematics and Science, NHCTC, HsinChu, Taiwan, In PressGoogle Scholar
  13. Chang T-H, Huang Y-Y, Jeng J-C, Kuo K-H: On property and related topics. Journal of Mathematical Analysis and Applications 1999,229(1):212–227. 10.1006/jmaa.1998.6154MATHMathSciNetView ArticleGoogle Scholar
  14. Chang S-S, Lee BS, Wu X, Cho YJ, Lee GM: On the generalized quasi-variational inequality problems. Journal of Mathematical Analysis and Applications 1996,203(3):686–711. 10.1006/jmaa.1996.0406MATHMathSciNetView ArticleGoogle Scholar
  15. Ding XP: Generalized theorems in generalized convex spaces and their applications. Journal of Mathematical Analysis and Applications 2002,266(1):21–37. 10.1006/jmaa.2000.7207MATHMathSciNetView ArticleGoogle Scholar


© Chi-Ming Chen et al. 2007

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.