About this document
Simple Proof of Banach Contraction Principle by James Tesen Garay is a document available to read on EtoBox.
The document provides a simple proof of the Banach contraction principle. It begins by defining a contraction mapping on a metric space and establishes the fundamental contraction inequality. It then shows that the iterates of a contraction mapping form a Cauchy sequence, and thus converge in a complete metric space. This proves that a contraction mapping has a unique fixed point. The document concludes by providing a stopping rule for numerical approximations of the fixed point.
- Author
- James Tesen Garay
- Language
- EN