contractive mapping

A contractive mapping is a mathematical concept where a function brings points closer together. Imagine points on a map: if you take a point and apply a contractive mapping, the new point will always be nearer to another point than it was before. This process continues, ensuring that repeated applications of the function lead to a single, stable point known as a fixed point. Contractive mappings are important in various fields, including analysis and computer science, particularly in showing that certain processes will converge to a solution or stable state.