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Theory of Topological Degree and Fixed Point Theorems in Fuzzy Normed Space
Author: LuYing
Tutor: XiaoJianZhong
School: Nanjing University of Information Engineering
Course: Applied Mathematics
Keywords: fuzzy normed space topological degree fixed point F1compact mapping multivalued mapping
CLC: O177.91
Type: Master's thesis
Year: 2007
Downloads: 80
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Abstract
This dissertation is devoted to the generalized topological degree of Apropermapping, fixed point theorems of FIcompact 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 LeraySchauder topological degree and its fixed pointtheorems in fuzzy normed space are introduced.In Chapter 3, the definition and properties of generalized topological degree ofAproper mapping in fuzzy normed space are given. Since the Aproper mapping isone of the extensions of compact mapping campus, whose generalized topologicaldegree is one of the extensions of LeraySchauder topological degree. Based on this,some fixed points for F_{1}compact mapping in fuzzy normed space are also established. We extend some fixed point theorems in Chapter 2 to F_{1}com pact mapping,such as Schauder, Altman fixed point theorems for the compact operators, etc.In Chapter 4, the definitions of closed and semicontinuous 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.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Nonlinear Functional Analysis
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