Contraction Mappings

Banach’s Contraction-Mapping Principle
  • Joel H. Shapiro
Part of the Universitext book series (UTX)


In this chapter we’ll study the best-known of all fixed-point theorems: the Banach Contraction-Mapping Principle, which we’ll apply to Newton’s Method, initial-value problems, and stochastic matrices.Prerequisites. Undergraduate-level real analysis and linear algebra. The basics of metric spaces: continuity and completeness.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Joel H. Shapiro
    • 1
  1. 1.Portland State UniversityPortlandUSA

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