Difference between revisions of "Delta Gronwall inequality"

Revision as of 00:34, 15 September 2016

Theorem

Let $y$ and $f$ be rd-continuous and $p$ be positively regressive and $p \geq 0$. If for all $t \in \mathbb{T}$ $$y(t) \leq f(t) + \displaystyle\int_a^t y(\tau) p(\tau) \Delta \tau,$$ then $$y(t) \leq f(t) + \displaystyle\int_a^t e_p(t,\sigma(\tau))f(\tau)p(\tau)\Delta \tau$$ for all $t \in \mathbb{T}$.

Proof

References

Ravi Agarwal, Martin Bohner and Allan Peterson: Inequalities on Time Scales: A Survey (2001)... (previous)... (next): Theorem 5.6