Difference between revisions of "Rd-continuous"
From timescalewiki
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=Properties= | =Properties= | ||
[[Continuous implies rd-continuous]]<br /> | [[Continuous implies rd-continuous]]<br /> | ||
| + | [[rd-continuous implies regulated]]<br /> | ||
=References= | =References= | ||
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Regulated function|next=Continuous implies rd-continuous}}: Definition $1.58$ | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Regulated function|next=Continuous implies rd-continuous}}: Definition $1.58$ | ||
Revision as of 23:26, 4 January 2017
Let $\mathbb{T}$ be a time scale and $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a regulated function. We say that $f$ is rd-continuous if for any right dense point $t \in \mathbb{T}$, $f(t) = \displaystyle\lim_{\xi \rightarrow t^+} f(\xi)$. In other words, $f$ is rd-continuous if it is regulated and continuous at right dense points. The notation $C_{\mathrm{rd}}(\mathbb{T},X)$ denotes the set of rd-continuous functions $g \colon \mathbb{T} \rightarrow X$. We denote the set of rd-continuous functions that are $n$-times delta differentiable by the notation $C_{\mathrm{rd}}^n(\mathbb{T},X)$.
Properties
Continuous implies rd-continuous
rd-continuous implies regulated
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Definition $1.58$
