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      Fixed Point Theorems, Coincidence Point Theorems and Their Applications

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      SONAALLAH-THESIS-2016.pdf (352.9Kb)
      Date
      2016-09-26
      Author
      Sonaallah, Fatma 1986-
      Type
      Thesis
      Degree Level
      Masters
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      Abstract
      This study aims to illuminate a general framework for fixed point and coincidence point theorems. Our theorems work with functions defined on ball spaces (X,\cB). This notion provides the minimal structure that is needed to express the basic assumptions which are used in the proofs of such theorems when they are concerned with functions that are contractive in some way. We present a general fixed point theorem which can be seen as the underlying principle of proof for fixed point theorems of Banach and of Prie{\ss}-Crampe and Ribenboim. Also we study two types of general coincidence point theorems and their applications to metric spaces (Theorem due to K.~Goebel) and ultametric spaces (Theorem due to Prie{\ss}-Crampe and Ribenboim). Further, we find an alternative approach to coincidence point theorems. We introduce a general B_x theorem which does not deal with obtaining a coincidence point for two functions f,g directly, but allows a variety of applications. Then we present two coincidence point theorems as its applications. Finally, we introduce three different coincidence point theorems for ultrametric spaces. These theorems are: a special case of one of the general B_x theorem's applications, a coincidence point theorem due to Prie{\ss}-Crampe and Ribenboim, and an ultrametric version of Goebel's theorem. We study the logical relation between these theorems.
      Degree
      Master of Science (M.Sc.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Kuhlmann, Franz-Viktor
      Committee
      Wang, Jiun-Chau (JC); Netzer , Tim; Samei, Ebrahim
      Copyright Date
      October 2016
      URI
      http://hdl.handle.net/10388/7491
      Subject
      fixed point theorems
      coincidence point theorems
      ball space
      metric space
      ultrametric space.
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