# Difference between revisions of "Rd-continuous"

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=Properties= | =Properties= | ||

[[Continuous implies rd-continuous]]<br /> | [[Continuous implies rd-continuous]]<br /> | ||

+ | [[rd-continuous implies regulated]]<br /> | ||

+ | [[Forward jump is rd-continuous]]<br /> | ||

=References= | =References= | ||

− | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Regulated | + | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Regulated|next=Continuous implies rd-continuous}}: Definition $1.58$ |

+ | * {{PaperReference|Functional series on time scales|2008|Dorota Mozyrska|author2=Ewa Pawluszewicz|prev=Regulated|next=Pre-differentiable}} |

## Latest revision as of 14:53, 21 October 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

Forward jump is rd-continuous

# References

- Martin Bohner and Allan Peterson:
*Dynamic Equations on Time Scales*(2001)... (previous)... (next): Definition $1.58$ - Dorota Mozyrska and Ewa Pawluszewicz:
*Functional series on time scales*(2008)... (previous)... (next)