Existence Theorem Of Essential Components And It's Application

In this thesis, we discuss the unified existence theorem of essential components and the stability of generalized KKM points.It consists of three chapters.Chapter 1. Preliminaries. First, we recall some notions and results including Hausdorff distance and Baire's category. Second, we introduce KKM lemma and generalized KKM lemma. Finally, the semi-continuity, closure and compactness of set-valued mappings are introduced.Chapter2. Unified existence theorem of essential components. Yu et al. (2004) gave a unified existence theorem of essential components and deduced both the existence of essential components of the set of fixed points and that of the set of Nash equilibrium points. In this chapter, we improve some conditions of their unified theorem and obtain a new unified existence theorem of essential components. As applications, we deduce the existence of essential components of the set of the KKM points as well as the existence of essential components of the set of Ky Fan's points, Nash equilibrium points and fixed points respectively.Chapter3. Stability of generalized KKM points. We define a kind of generalized mappings and discuss the stability of their solutions. Our results include Yu and Xiang(2003)...