Theory Of Topological Degree And Fixed Point Theorems In Fuzzy Normed Space

This dissertation is devoted to the generalized topological degree of A-propermapping, fixed point theorems of FI-compact mapping and Kakutani fixed pointtheorem of multivalued mapping in fuzzy normed space.The paper is organized in the following manner.In Chapter 1, some known notions and results for fuzzy normed space arerecalled, such as linearly topological structure and some properties.In Chapter 2, the Leray-Schauder topological degree and its fixed pointtheorems in fuzzy normed space are introduced.In Chapter 3, the definition and properties of generalized topological degree ofA-proper mapping in fuzzy normed space are given. Since the A-proper mapping isone of the extensions of compact mapping campus, whose generalized topologicaldegree is one of the extensions of Leray-Schauder topological degree. Based on this,some fixed points for F₁-compact mapping in fuzzy normed space are also establi-shed. We extend some fixed point theorems in Chapter 2 to F₁-com pact mapping,such as Schauder, Altman fixed point theorems for the compact operators, etc.In Chapter 4, the definitions of closed and semi-continuous multivaluedmapping in fuzzy normed space are introduced. By establishing Schauder fixed pointtheorem in fuzzy normed space, the extension of Kakutani fixed point theorem inthis space is obtained.