在本篇論文中，我們利用超凸度量空間的性質證明了可允許集的交集性質。利用這個性質，我們證得一個推廣型 定理、一個匹配定理及一個同值點定理。在應用方面，我們利用這個推廣型 定理，證明一些變分不等式及大中取小不等式的存在性定理。

In this paper, we use the property of hyperconvex metric space to establish an intersection property about a family of admissible sets. Applying this intersection property we get a generalized theorem, a matching theorem and a coincidence theorem. As the application, we use this generalized theorem to establish some existence theorems about variational inequalities and minimax inequalities.

[1] A. Amini, M. Fakhar, and J. Zafarani, KKM mappings in metric spaces, Nonlinear Anal. 60(2005), 1045-1052.
[2] N. Aronszajn, and P. Panitchpakdi, Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6(1956) 405-439.
[3] K. C. Border, Fixed point theorems with applications to economics and game theory, Cambridge University Press, 1989.
[4] S. S. Chang and Y. Zhang, Generalized KKM theorem and variational inequalities, J. Math. Anal. Appl. 159(1991), 208-233.
[5] T. H. Chang and C. L. Yen, KKM property and fixed point theorems, J. Math. Anal. Appl. 203(1996), 224-235.
[6] L. A. Dung and D. H. Tan, Some applications of the KKM-mapping principle in hyperconvex metric spaces, Nonlinear Ana, to appear.
[7] X. P. Ding, Y. C. Liou, and J. C. Yao, Generalized R-KKM type theorems in topological spaces with applications, Appl. Math. Letters. 18(2005), 1345-1350.
[8] K. Fan, A generalization of Tychonoff’s fixed point theorem, Math. Ann. 142(1961),305-310.
[9] K. Fan, Some properties of convex sets related to fixed point theorem, Math. Ann. 266(1984), 519-537.
[10] B. Knaster, C. Kuratowski, and S. Mazurkiewicz, Ein Beweis des Fixpunksatzes fur n-dimensionale simplexe, Fund. Math. 14(1929),132-137.
[11] M. A. Khamsi, KKM and Ky Fan Theorems in Hyperconvex Metric Spaces, J. Math. Anal. Appl. 204(1996),298-306.
[12] W. A. Kirk, B. Sims, and G. X .Z. Yuan, The Knaster-Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications, Nonlinear Anal. 39(2000), 611-627.
[13] L. J. Lin and W. P. Wan, KKM type theorems and coincidence theorems with applications to the existence of equilibria, J. Optim. Theory Appl. 123(1)(2004), 105-122.
[14] J. T. Markin, A selection theorem for quasi-lower semicontinuous mappings in hyperconvex spaces, J. Math. Anal. Appl. 321(2006), 862-866.
[15] S. Park, Fixed point theorems in hyperconvex metric spaces, Nonlinear Anal. 37(1999), 467-472.
[16] N. Shioji, A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem, Proc. Amer. Math. Soc. 111(1991), 187-195.
[17] G. Q. Tina, Generalized KKM theorem, minimax inequalities and their applications, J. Optim. Theory Appl. 83(1994), 375-389.
[18] N. T. Vinh, Matching theorems, fixed point theorems and minimax inequalities in topological ordered spaces, Acta. Math. Vietnamica. 30(2005), 211-224.
[19] X. Wu, B. Thompson, and G. X. Yuan, Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces, J. Math. Anal. Appl. 276(2002), 80-89.
[20] G. X. Z. Yuan, The Charactreization of Generalized Metric KKM Mappings with Open Values in Hyperconvex Metric Spaces and Some Applications, J. Math. Anal. Appl. 235(1999), 315-325.