Difference between revisions of "Delta Bernoulli inequality"
From timescalewiki
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{{PaperReference|Inequalities on Time Scales: A Survey|2001|Ravi Agarwal|author2 = Martin Bohner| author3 = Allan Peterson|prev=findme|next=findme}}: Theorem 5.5 | {{PaperReference|Inequalities on Time Scales: A Survey|2001|Ravi Agarwal|author2 = Martin Bohner| author3 = Allan Peterson|prev=findme|next=findme}}: Theorem 5.5 | ||
| − | {{:Delta inequalities footer}} | + | <center>{{:Delta inequalities footer}}</center> |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 15:45, 21 January 2023
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.
Proof
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 |
