arithmetic-geometric mean inequality
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:alsoKnownAs |
gptkb:AM-GM_inequality
|
| gptkbp:appliesTo |
non-negative real numbers
|
| gptkbp:equalityCondition |
Equality holds if and only if all the numbers are equal.
|
| gptkbp:field |
gptkb:algebra
gptkb:mathematics analysis |
| gptkbp:firstPublished |
18th century
|
| gptkbp:form |
(a_1 + a_2 + ... + a_n)/n ≥ (a_1 * a_2 * ... * a_n)^{1/n}
|
| gptkbp:generalizes |
power mean inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
arithmetic-geometric mean inequality
|
| gptkbp:proofMethods |
gptkb:Lagrange_multipliers
gptkb:Jensen's_inequality induction |
| gptkbp:relatedTo |
gptkb:Cauchy-Schwarz_inequality
gptkb:Holder's_inequality gptkb:Jensen's_inequality |
| gptkbp:state |
For any non-negative real numbers, the arithmetic mean is greater than or equal to the geometric mean.
|
| gptkbp:usedIn |
gptkb:mathematical_olympiads
optimization inequality proofs |
| gptkbp:bfsParent |
gptkb:Young's_inequality
|
| gptkbp:bfsLayer |
4
|