Difference between revisions of "Delta Opial inequality"

Revision as of 00:35, 15 September 2016

Theorem

For a differentiable $x \colon [0,h] \cap \mathbb{T} \rightarrow \mathbb{R}$ with $x(0)=0$ we have $$\displaystyle\int_0^h |(x+x^{\sigma})x^{\Delta}|(t) \Delta t \leq h \displaystyle\int_0^h |x^{\Delta}|^2(t) \Delta t,$$ with equality when $x(t)=ct$.

Proof

References

Ravi Agarwal, Martin Bohner and Allan Peterson: Inequalities on Time Scales: A Survey (2001)... (previous)... (next): Theorem 6.1