# Difference between revisions of "Delta Gronwall inequality"

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==References== | ==References== | ||

− | + | {{PaperReference|Inequalities on Time Scales: A Survey|2001|Ravi Agarwal|author2 = Martin Bohner| author3 = Allan Peterson|prev=findme|next=findme}}: Theorem 5.6 | |

{{:Delta inequalities footer}} | {{:Delta inequalities footer}} |

## 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

## $\Delta$-Inequalities

Bernoulli | Bihari | Cauchy-Schwarz | Gronwall |
Hölder | Jensen | Lyapunov | Markov | Minkowski | Opial | Tschebycheff | Wirtinger |