# Difference between revisions of "Delta Cauchy-Schwarz inequality"

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==Theorem== | ==Theorem== | ||

Let $a,b \in \mathbb{T}$. For [[continuity | rd-continuous]] $f,g \colon [a,b]\cap \mathbb{T} \rightarrow \mathbb{R}$ we have | Let $a,b \in \mathbb{T}$. For [[continuity | rd-continuous]] $f,g \colon [a,b]\cap \mathbb{T} \rightarrow \mathbb{R}$ we have |

## Revision as of 00:30, 15 September 2016

## Theorem

Let $a,b \in \mathbb{T}$. For rd-continuous $f,g \colon [a,b]\cap \mathbb{T} \rightarrow \mathbb{R}$ we have $$\displaystyle\int_a^b |f(t)g(t)| \Delta t \leq \sqrt{\left( \displaystyle\int_a^b |f(t)|^2 \Delta t \right) \left( \displaystyle\int_a^b |g(t)|^2 \Delta t \right)}$$

## Proof

## References

Ravi Agarwal, Martin Bohner and Allan Peterson: *Inequalities on Time Scales: A Survey* (2001)... (previous)... (next): Theorem 3.2

## $\Delta$-Inequalities

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