Difference between revisions of "Delta Bernoulli inequality"

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__NOTOC__
<strong>Theorem:</strong> Let $\alpha \in \mathbb{R}$ be a [[Regressive_function | positively regressive]] constant. Then
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==Theorem==
$$e_{\alpha} \geq 1 + \alpha(t-s)$$
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Let $\mathbb{T}$ be a [[time scale]] and $\alpha \in \mathbb{R}$ be a [[Regressive_function | positively regressive]] constant. Then for all $t,s \in \mathbb{T}$
for all $t,s \in \mathbb{T}$.
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$$e_{\alpha} \geq 1 + \alpha(t-s),$$
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where $e_{\alpha}$ denotes the [[delta exponential]].
<strong>Proof:</strong> █
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==Proof==
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==References==
 
==References==
[http://www.math.unl.edu/~apeterson1/pub/ineq.pdf R. Agarwal, M. Bohner, A. Peterson - Inequalities on Time Scales: A Survey]
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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
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{{:Delta inequalities footer}}
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest 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

$\Delta$-Inequalities

Bernoulli Bihari Cauchy-Schwarz Gronwall Hölder Jensen Lyapunov Markov Minkowski Opial Tschebycheff Wirtinger