\begin{definition}[Definition:Extremum/Functional]
Let $S$ be a set of mappings.
Let $J \sqbrk y: S \to \R$ be a functional.
Let $y, \hat y: \R \to \R$ be real functions.
Suppose for $y = \hat y \paren x$ there exists a neighbourhood of the curve $y = \hat y \paren x$ such that the difference $J \sqbrk y - J \sqbrk {\hat y}$ does not change its sign in this neighbourhood.
Then $y = \hat y$ is called a ('''relative''') '''extremum''' of the functional $J$.
{{Help|Check if "some neighbourhood" could be more precisely defined |user = Julius}}
\end{definition}