Fixed points (mathematics)

In mathematics, a fixed point of a function is a point that is mapped to itself by that function. More formally, if \( f \) is a function and \( x \) is an element of its domain, then \( x \) is a fixed point of \( f \) if: \[ f(x) = x \] Fixed points are important in various areas of mathematics, including analysis, topology, and differential equations.