Difference between revisions of "Delta derivative at right-scattered"

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==References==
 
==References==
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta differentiable implies continuous|next=Delta derivative at right-dense}}: Theorem 1.16
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* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta differentiable implies continuous|next=Delta derivative at right-dense}}: Theorem 1.16 (ii)
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 15:18, 21 January 2023

Theorem

Let $\mathbb{T}$ be a time scale. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be continuous and right-scattered at $t \in \mathbb{T}$. Then $$f^{\Delta}(t)=\dfrac{f(\sigma(t))-f(t)}{\mu(t)},$$ where $f^{\Delta}$ denotes the delta derivative, $\sigma$ denotes the forward jump, and $\mu$ denotes the forward graininess.

Proof

References