摘要
本論文主要探討一些固定點定理以及一些推廣型KKM定理，並將這些結果應用到一些相關課題上。如：匹配定理、擬平衡點、擬變分不等式等。
本論文共分為三章，第一章探討有關向內地(inward)收縮和非擴張函數的固定點定理以及二函數的同值點定理。第二章則先引入一些非凸集合，探討其性質，再進而探討在這些非凸集合上的一些推廣型S-KKM定理、匹配定理、擬平衡點存在性定理等。在本章中並引入一個新的函數族：Q(X,Y)，探討其性質及相關定點定理。第三章則探討在均勻空間上可逼近(approachable )函數族的一些性質，及固定點定理以及二函數的同值點定理。
本論文內容主要藉由探討近年來一些學者的相關論著，並引入一些新的函數族，探討其性質，進一步推導出更廣的結果，這些結果涵蓋了許多學者的一些結果。

The purpose of this paper is to study the fixed point theory and the KKM theory , we get some fixed point theorems and generalized KKM theorems. As applications, we use the above results to related topics, for examples, the matching theorems, the existence theorems of quasi-equilibrium, quasi-variational inequalities.
This paper contains three chapters. In the first chapter, we discuss some fixed point theorems and coincidence theorems about inward contractive functions and inward nonexpansive functions. In second chapter, we introduce some conceptions of non-convexities, study their properties, and apply these properties to get some generalized KKM theorems, the matching theorems, and the existence theorems of quasi-equilibrium. In this chapter, we also introduce a new family of functions, Q(X,Y), we research its properties and get some fixed point theorems about this family. In the last chapter, we study the properties of the family of approachable functions in uniform spaces. By using these properties, we attain some fixed point theorems and coincidence theorems.
The results of this paper actually extend many results of authors as in the references.

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