arithmetic mean-geometric mean inequality
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:abbreviation |
gptkb:AM-GM_inequality
|
| gptkbp:appliesTo |
non-negative real numbers
|
| gptkbp:category |
Inequalities
|
| gptkbp:describes |
relationship between arithmetic mean and geometric mean
|
| gptkbp:equality_holds_when |
all numbers are equal
|
| gptkbp:expressedIn |
(a1 + a2 + ... + an)/n ≥ (a1*a2*...*an)^(1/n)
|
| gptkbp:field |
gptkb:algebra
gptkb:mathematics analysis |
| gptkbp:firstPublished |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:generalizes |
power mean inequality
|
| gptkbp:hasSpecialCase |
gptkb:Jensen's_inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
arithmetic mean-geometric mean inequality
|
| gptkbp:relatedTo |
gptkb:Cauchy-Schwarz_inequality
gptkb:Holder's_inequality gptkb:Jensen's_inequality |
| gptkbp:state |
arithmetic mean of non-negative real numbers is greater than or equal to their geometric mean
|
| gptkbp:used_in |
optimization
proofs inequality theory |
| gptkbp:bfsParent |
gptkb:Cauchy–Schwarz_inequality
|
| gptkbp:bfsLayer |
6
|