\begin{definition}[Definition:Differentiable Functional]
Let $S$ be a normed linear space of mappings.
Let $y, h \in S: \R \to \R$ be real functions.
Let $J \sqbrk y$, $\phi \sqbrk {y; h}$ be functionals.
Let $\Delta J \sqbrk {y; h}$ be an increment of the functional $J$ such that:
:$\Delta J \sqbrk {y; h} = \phi \sqbrk {y;h} + \epsilon \norm h$
where $\epsilon = \epsilon \sqbrk {y; h}$ is a functional, and $\norm h$ is the norm of $S$.
Suppose $\phi \sqbrk {y; h}$ is a linear {{WRT}} $h$ and:
:$\ds \lim_{\norm h \mathop \to 0} \epsilon = 0$
Then the functional $J \sqbrk y $ is said to be '''differentiable'''.
\end{definition}