\begin{definition}[Definition:Increment/Functional]
Let $S$ be a set of mappings.
Let $y, h: \R \to \R$ be real functions.
Let $J \sqbrk y: S \to \R$ be a functional defined on a normed vector space.
Consider the following difference:
:$ \Delta J \sqbrk {y; h} = J \sqbrk {y + h} - J \sqbrk y$
Then $\Delta J \sqbrk {y; h}$ is known as the '''increment of the functional $J$'''.
\end{definition}