Definition:Increment/Functional

Definition
Let $S$ be a set of mappings.

Let $y,h:\R\rightarrow\R$ be real functions.

Let $ J \left [ { y } \right ] : S \to \R $ be a functional defined on a normed linear 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 $.

Also defined as
For fixed y an increment of the functional $ J $  is only a functional of $ h $ and is denoted by $\Delta J[h]$.