Contractive Mappings

A contractive mapping is a mathematical function that brings points closer together with each application. More precisely, when you apply the function to two different points, the distance between their images is always less than their original distance by a consistent factor less than one. This property guarantees that repeated application of the function on any starting point will eventually lead to a single, fixed point where the input and output are the same. Contractive mappings are important because they ensure convergence and stability in various mathematical and computational processes, such as solving equations or modeling dynamic systems.