在這篇論文中，我們建立一些在殆凸集合上 集族的固定點定理，而且我們利用這些集族和 -映射進而求得同質點定理。

In this paper, we establish some fixed point theorems for the family on an almost-convex set without compactness assumption, and then we get the coincidence theorem for this family and the -mapping.

[1] T. H. Chang, Y. Y. Huang, J. C. Jeng ,K. H. Kuo, On S-KKM property and related topics, J. Math. Anal. Appl. 229(1999), 212-227.
[2] T. H. Chang, C. L. Yen, KKM property and fixed point theorems,
J. Math. Anal. Appl.203(1996), 224-235.
[3] C. M. Chen, T. H. Chang, C. W. Chung, Coincidence theorems on nonconvex sets and its applications, Taiwanese Journal of Mathematics, in press.
[4] P.M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems for multival- ued noncompact inward mappings, J. Math. Anal. Appl. 46(1974), 756-767.
[5] J. C. Jeng, H. C. Hsu, Y. Y. Huang, Fixed point theorems for multifunc- tions having KKM property on almost convex sets. J. Math. Anal. Appl.
319(2006), 187-198.
[6] Ky Fan, A generalization of Tychonoff ’s fixed point theorem, Math. Ana142(1961), 305-310.
[7] B. Knaster, C. Kuratowski, S. Mazurkiewicz, Ein Beweis des Fixpunksatzes fur n-dimensionale Simplexe, Fund. Math.14(1929), 132-137.
[8] M. Lassonde, Fixed point for Kakutai factorizable multifunctions, J. Math. Anal. Appl. 152(1990), 46-60.
[9] L. J. Lin, Applications of a fixed point theorems in G-convex spaces, Nonlinear Anal. 46(2001), 601-608.
[10] L. J. Lin, System of coincidence theorems with applications, J. Math. Anal. Appl. 285(2003), 408-418.
[11] G. J. Minty, On the maximal domain of a monotone function, Michigan Math. J. 8(1961), 179-182.
[12] W. V. Petryshyn, P. M. Fitzpatrick, A degree theory, fixed point theorems and matching theorems for noncompact mappings, Trans. Amer. Math. Soc. (to appear).
[13] G. Q. Tian,Generalizations of KKM theorem and ky Fan minmax inequality with applications to maximal elements, price equilibrium and complementarity, J. Math. Anal. Appl. 170(1992), 457-471.