Difference between revisions of "Delta Bernoulli inequality"

From timescalewiki
Jump to: navigation, search
Line 10: Line 10:
 
{{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 AgarwalMartin Bohner and Allan Peterson: Inequalities on Time Scales: A Survey (2001)... (previous)... (next): Theorem 5.5

<center>

$\Delta$-Inequalities

Bernoulli Bihari Cauchy-Schwarz Gronwall Hölder Jensen Lyapunov Markov Minkowski Opial Tschebycheff Wirtinger
</center>