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

Abstract

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

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References

  1. Knaster B, Kurnatoaski C, Mazurkiewicz S: Ein Beweis des Fixpunksatzes fur -dimensionale simplexe. Fundamenta Mathematicae 1929, 14: 132–137.

    MATH  Google Scholar 

  2. Fan K: A generalization of Tychonoff's fixed point theorem. Mathematische Annalen 1961, 142: 305–310. 10.1007/BF01353421

    Article  MATH  MathSciNet  Google 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.1996.0376

    Article  MATH  MathSciNet  Google 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.

    MATH  MathSciNet  Google 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/S1085337503210034

    Article  MATH  Google 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)00329-6

    Article  MATH  Google 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)00687-6

    Article  MATH  MathSciNet  Google 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.1996.0014

    Article  MATH  MathSciNet  Google 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)00108-1

    Article  MATH  MathSciNet  Google 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)00406-2

    Article  MATH  MathSciNet  Google Scholar 

  12. Chang T-H, Lee YL: theorem and its applications. J. Graduate Institute of Mathematics and Science, NHCTC, HsinChu, Taiwan, In Press

  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.1998.6154

    Article  MATH  MathSciNet  Google 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.1996.0406

    Article  MATH  MathSciNet  Google 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.2000.7207

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Chi-Ming Chen.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Chen, CM., Chang, TH. & Liao, YP. Coincidence Theorems, Generalized Variational Inequality Theorems, and Minimax Inequality Theorems for the -Mapping on -Convex Spaces. Fixed Point Theory Appl 2007, 078696 (2007). https://doi.org/10.1155/2007/78696

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  • DOI: https://doi.org/10.1155/2007/78696

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