Delta Bernoulli inequality

Theorem: Let $\alpha \in \mathbb{R}$ be a positively regressive constant. Then $$e_{\alpha} \geq 1 + \alpha(t-s)$$ for all $t,s \in \mathbb{T}$.

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