09/05/10 21:46:04
〔問題〕
a,b,c,p,q >0, 1/2 ≦ p/q ≦ 2 のとき
a/(pb+qc) + b/(pc+qa) + c/(pa+qb) ≧ (p+q)^2 (a+b+c)^3 /{9(pb+qc)(pc+qa)(pa+qb)}
≧ (1/3)(a+b+c){1/(pb+qc) + 1/(pc+qa) + 1/(pa+qb)}
≧ 3/(p+q),
(Shapiro不等式の一拡張)
09/05/10 21:46:04
〔問題〕
a,b,c,p,q >0, 1/2 ≦ p/q ≦ 2 のとき
a/(pb+qc) + b/(pc+qa) + c/(pa+qb) ≧ (p+q)^2 (a+b+c)^3 /{9(pb+qc)(pc+qa)(pa+qb)}
≧ (1/3)(a+b+c){1/(pb+qc) + 1/(pc+qa) + 1/(pa+qb)}
≧ 3/(p+q),
(Shapiro不等式の一拡張)