Difference between revisions of "Delta Gronwall inequality"

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[http://www.math.unl.edu/~apeterson1/pub/ineq.pdf R. Agarwal, M. Bohner, A. Peterson - Inequalities on Time Scales: A Survey]
{{PaperReference|Inequalities on Time Scales: A Survey|2001|Ravi Agarwal|author2 = Martin Bohner| author3 = Allan Peterson|prev=findme|next=findme}}: Theorem 5.6
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Revision as of 00:34, 15 September 2016


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 $t \in \mathbb{T}$.



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


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