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Fixed Point Theorems and Applications

  • Hervé Le Dret
Chapter
  • 2.5k Downloads
Part of the Universitext book series (UTX)

Abstract

If f is a mapping from a set E into itself, any element x of E such that f(x) = x is called a fixed point of f. Many problems, including nonlinear partial differential equations problems, may be recast as problems of finding a fixed point of a certain mapping in a certain space. We will see several examples of this a little later on. It is therefore interesting to have fixed point theorems at our disposal that are as general as possible.

Keywords

Fixed Point Theorem Asserts Linear Existence Closed Unit Ball Leray Schauder Accessible Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hervé Le Dret
    • 1
  1. 1.Laboratoire Jacques-Louis LionsSorbonne UniversitéParisFrance

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