Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
non-negative real numbers
|
| gptkbp:category |
inequalities involving symmetric sums
|
| gptkbp:field |
gptkb:algebra
inequality theory |
| gptkbp:firstPublished |
1916
|
| gptkbp:form |
For real numbers x, y, z ≥ 0 and r ≥ 0: x^r(x−y)(x−z) + y^r(y−x)(y−z) + z^r(z−x)(z−y) ≥ 0
|
| gptkbp:generalizes |
gptkb:Muirhead's_inequality
|
| gptkbp:hasSpecialCase |
when r=1: x(x−y)(x−z) + y(y−x)(y−z) + z(z−x)(z−y) ≥ 0
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schur's inequality
|
| gptkbp:namedAfter |
gptkb:Issai_Schur
|
| gptkbp:relatedTo |
gptkb:AM-GM_inequality
gptkb:Nesbitt's_inequality |
| gptkbp:usedIn |
olympiad mathematics
symmetric inequalities |
| gptkbp:bfsParent |
gptkb:William_Schur
|
| gptkbp:bfsLayer |
6
|