Delta mean value theorem
From timescalewiki
Revision as of 23:53, 4 January 2017 by Tom (talk | contribs) (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ be pre-differentiable with $D$. Then $|f^{\Delta}(t)| \leq g^{\Delt...")
Theorem
Let $\mathbb{T}$ be a time scale and let $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ be pre-differentiable with $D$. Then $|f^{\Delta}(t)| \leq g^{\Delta}(t)$ for all $t \in \mathbb{T}$ implies $$|f(s)-f(r)| \leq g(s)-g(r)$$ for all $r,s \in \mathbb{T}$ with $r \leq s$.
Proof
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Theorem $1.67$
