Difference between revisions of "Delta Jensen inequality"

Latest revision as of 00:36, 15 September 2016

Theorem

Let $a,b \in \mathbb{T}$ and $c,d \in \mathbb{R}$. Suppose $g \colon [a,b]\cap \mathbb{T} \rightarrow (c,d)$ is rd-continuous and $F \colon (c,d) \rightarrow \mathbb{R}$ is convex. Then $$F \left(\dfrac{\displaystyle\int_a^b g(t) \Delta t}{b-a}\right) \leq \dfrac{\displaystyle\int_a^b F(g(t))\Delta t}{b-a}.$$

Proof

References

Ravi Agarwal, Martin Bohner and Allan Peterson: Inequalities on Time Scales: A Survey (2001)... (previous)... (next): Theorem 4.1