Difference between revisions of "Pre-differentiable"
From timescalewiki
(Created page with "Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mat...") |
|||
| Line 1: | Line 1: | ||
Let $\mathbb{T}$ be a [[time scale]] and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mathbb{T}^{\kappa}$ if $f$ id [[delta derivative|delta differentiable]] at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no [[scattered point|right-scattered]] points in $\mathbb{T}$. | Let $\mathbb{T}$ be a [[time scale]] and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mathbb{T}^{\kappa}$ if $f$ id [[delta derivative|delta differentiable]] at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no [[scattered point|right-scattered]] points in $\mathbb{T}$. | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=findme|next=findme}}: Definition $1.62$ | ||
Revision as of 23:41, 4 January 2017
Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mathbb{T}^{\kappa}$ if $f$ id delta differentiable at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no right-scattered points in $\mathbb{T}$.
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Definition $1.62$
