在這篇論文中，我們首先在一完備度量空間之有界凸子集上探討一個收縮函數的定點定理。其次，我們在這一條件下得到一些同質點定理，匹配定理及變分不等式。

In this paper, we first establish the fixed-point theorem for k-set contraction map on a bounded subadmissible subset of a complete metric space, which not need a compact map. Next, we get some coincidence theorems, matching theorems and variational inequalities on this class.

第一章 緒論…………………………………………………………1
第二章 主定理說明…………………………………………………4
第三章 應用…………………………………………………………7
第四章 參考文獻……………………………………………………11

[1] A. Amimi, M. Fakhar, J. Zafarni, KKM mappings in metric spaces, Nonlinear Analysis, 60(2005), 1045-1052.
[2] T. H. Chang, C. L. Yen, KKM property and fixed point theorems, J. Math. Ann. Appl, 203(1996), 224-235.
[3] Ky Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann, 142(1961), 305-310.
[4] B. Knaster, C. Kuratowski, S. Mazurkiewicz, Ein Beweis des Fixpunksatzes fur n-dimensionale Simplexe, Fund. Math, 14(1929), 132-137.
[5] M. A. Khamsi, KKM and Ky Fan theorems in hyperconvex spaces, J. Math. Ann. Appl, 204(1996), 298-306.
[6] R. Nussbaum. The fixed point index and fixed point theorems for k-set contractions, Doctoral Dissertation, University of Chicago (1969).