Definition:Functional/Real

Definition
Let $S$ be a set of mappings.

Let $J:S\to\R$ be a mapping:
 * $\forall y \in S: \exists x \in \R: J \sqbrk{y} = x$

Then $J:S\to\R$ is known as a functional, denoted by $J \sqbrk{y}$.

That is, a functional is a real-valued function whose arguments are themselves mappings.