Difference between revisions of "Delta derivative at right-dense"
From timescalewiki
(Created page with "==Theorem== Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}$ be right-dense. Then $f \colon \mathbb{T} \rightarrow \mathbb{R}$ is delta derivative|delta differen...") |
(No difference)
|
Revision as of 05:23, 10 June 2016
Theorem
Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}$ be right-dense. Then $f \colon \mathbb{T} \rightarrow \mathbb{R}$ is delta differentiable at $t$ if and only if the limit $$f^{\Delta}(t)=\displaystyle\lim_{s \rightarrow t} \dfrac{f(t)-f(s)}{t-s}$$ exists.
Proof
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Theorem 1.16
