【摘要】 给出了控制理论中非对称凸集D={x∈Rn:x1≥…≥xn}上的Schur凸函数判定定理的4个应用:1)证明了一个代数不等式,2)推广了一个平均值不等式,3)确定了一类加权平均的Schur凹性,4)验证了一个积函数Schur凸的充分必要条件.更多还原

【Abstract】 Four applications of the decision theorem for the Schur-convex function on the asymmetrical convex set D={x∈ Rn:x1≥…≥ xn} in the theory of majorization are given:1) an algebraic inequality is proved,2) a mean value inequality is extended,3) the Schur-concavity of a weighted means is determined,4) the necessary and sufficient condition that a product function is Schur-convex is verified.更多还原