几何、调和平均组合的最佳广义对数平均界

Optimal generalized logarithmic mean bounds for the combination of geometric and harmonic means

应用初等微分学知识,对几何平均、调和平均的几何组合与广义对数平均进行了比较,解决了如下问题:对于α∈(0,1),使双向不等式Lp(a,b)≤Gα(a,b)H1-α(a,b)≤Lq(a,b)对所有的a,b>0成立的最大p和最小q分别是多少?

It was compared the generalized logarithmic mean with the geometric combination of geometric and harmonic means by the elementary differential calculus. It was discussed for a∈（0,1） , the greatest value p and the least value q, such that the inequality Lp（0,6）≤G^ct（0,b）H^t-a（a,b）≤Lq（a,b） held for all a, b 〉0.