Difference between revisions of "Delta Minkowski inequality"

Latest revision as of 00:38, 15 September 2016

Theorem

Let $a,b \in \mathbb{T}$ and $p>1$. For rd-continuous $f,g \colon [a,b] \cap \mathbb{T} \rightarrow \mathbb{R}$ we have $$\left( \displaystyle\int_a^b |(f+g)(t)|^p \Delta t \right)^{\frac{1}{p}} \leq \left( \displaystyle\int_a^b |f(t)|^p \Delta t \right)^{\frac{1}{p}}+ \left( \displaystyle\int_a^b |g(t)|^p \Delta t\right)^{\frac{1}{p}}.$$

Proof

References

Ravi Agarwal, Martin Bohner and Allan Peterson: Inequalities on Time Scales: A Survey (2001)... (previous)... (next): Theorem 3.3