Contraction mappings

A contraction mapping is a type of function that brings points closer together in a predictable way. Specifically, when you apply the function to two points, the distance between their images is always less than the original distance by a certain factor less than one. This property ensures that, if you repeatedly apply the function starting from any point, the process will eventually settle at a single fixed point—meaning the function's output at that point is the same as the input. Contraction mappings are important in mathematics for proving the existence and uniqueness of solutions to equations.