Brouwer's Fixed Point Theorem: Methods of Proof and Applications

Stuckless, Tara (2003) Brouwer's Fixed Point Theorem: Methods of Proof and Applications. MSc Thesis thesis, Simon Fraser University.

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      The familiar Brouwer fixed point theorem says that any continuous self­map f on a compact convex subset X of finite dimensional Euclidean space E must leave at least one point fixed. This result is easy to state, but notoriously complicated to prove. We will give a sample of the various methods of proof available, ranging from the degree­theoretical methods used by Brouwer in the early 20th century, up to a recent proof based on an alternate change of variables formula for multiple integrals. We will also explore extensions of the theorem based on generalizations the space E, the set X, and the function f .

      Item Type: Thesis (MSc Thesis)
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: fixed point theory,
      Subjects: 47-xx Operator theory > 47Hxx Nonlinear operators and their properties
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 27 Oct 2003
      Last Modified: 21 Apr 2010 11:13

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