Difference between revisions of "Pre-differentiable"
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| − | 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 $f$ | + | 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 $f$ is [[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 $\mathbb{T}$. |
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| + | =Properties= | ||
=References= | =References= | ||
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=findme|next=Regulated on compact interval is bounded}}: Definition $1.62$ | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=findme|next=Regulated on compact interval is bounded}}: Definition $1.62$ | ||
* {{PaperReference|Functional series on time scales|2008|Dorota Mozyrska|author2=Ewa Pawluszewicz|prev=rd-continuous|next=findme}} | * {{PaperReference|Functional series on time scales|2008|Dorota Mozyrska|author2=Ewa Pawluszewicz|prev=rd-continuous|next=findme}} | ||
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| + | [[Category:Definition]] | ||
Latest revision as of 12:53, 16 January 2023
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 $f$ is delta differentiable at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no right-scattered points in $\mathbb{T}$.
Properties
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Definition $1.62$
- Dorota Mozyrska and Ewa Pawluszewicz: Functional series on time scales (2008)... (previous)... (next)
