Difference between revisions of "Delta Bernoulli inequality"
From timescalewiki
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__NOTOC__ | __NOTOC__ | ||
==Theorem== | ==Theorem== | ||
| − | Let $\alpha \in \mathbb{R}$ be a [[Regressive_function | positively regressive]] constant. Then | + | Let $\alpha \in \mathbb{R}$ be a [[Regressive_function | positively regressive]] constant. Then for all $t,s \in \mathbb{T}$ |
| − | $$e_{\alpha} \geq 1 + \alpha(t-s)$$ | + | $$e_{\alpha} \geq 1 + \alpha(t-s).$$ |
| − | |||
==Proof== | ==Proof== | ||
Revision as of 23:36, 14 September 2016
Theorem
Let $\alpha \in \mathbb{R}$ be a positively regressive constant. Then for all $t,s \in \mathbb{T}$ $$e_{\alpha} \geq 1 + \alpha(t-s).$$
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 |
