Delta Minkowski inequality

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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

R. Agarwal, M. Bohner, A. Peterson - Inequalities on Time Scales: A Survey

$\Delta$-Inequalities

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