Delta Bernoulli inequality

Theorem

Let $\mathbb{T}$ be a time scale and $\alpha \in \mathbb{R}$ be a positively regressive constant. Then for all $t,s \in \mathbb{T}$ $$e_{\alpha} \geq 1 + \alpha(t-s),$$ where $e_{\alpha}$ denotes the delta exponential.

References

Ravi Agarwal, Martin Bohner and Allan Peterson: Inequalities on Time Scales: A Survey (2001)... (previous)... (next): Theorem 5.5

$\Delta$-Inequalities

Bernoulli

Bihari

Cauchy-Schwarz

Gronwall

Hölder

Jensen

Lyapunov

Markov

Minkowski

Opial

Tschebycheff

Wirtinger