Definition:Fixed Point

Definition
Let $f: S \to T$ be a mapping.

Then a fixed point (or fixed element) of $S$ under $f$ is an $x \in S$ such that $f \left({x}\right) = x$.

Also defined as
The concept of a fixed point is usually encountered in the context of self-maps, that is, where $S = T$.

Also see

 * Definition:Fixed Element of Permutation