Fixed Points in Mathematics
Definition
A Fixed Point is said to be a $x_{0} \in X$ that satisfies the following condition for the function $f : X \to X$. $$ f \left( x_{0} \right) = x_{0} $$ When the derivative $f '$ of $f$ is given, the following is also referred to as a fixed point. $$ f ' \left( x_{0} \right) = 0 $$
Explanation
In universal mathematics, the concept of fixed points appears in numerous definitions and theorems, and it can be asserted that it touches the essence of mathematics due to its invariant nature with respect to the given function $f$.