加权幂平均值不等式的一个新证明

A New Proof of Weighted Power Mean Inequality

不同于文[1],笔者利用熟知的凹函数方法,给出了加权幂平均值不等式的一种新的证明。首先给出凹函数的一个性质作为引理,然后对引理中的不等式作简单的变换,就得到了待证的不等式。证明过程推导简洁,思路清晰。

Different from article[1],a new proof of weghted power mean inequality by applying the well-known concave function method is given here.First,a property of concave function as a lemma is presented.Then based on this lemma,it is proved that weighted power mean inequality is correct.In this proof,the inferential process is succinct and the statement is clear.