对算术-几何不等式的两种推广与改进

Two Improvements of Arithmetic-geometric Mean Inequality

将关于一组正数的加权算术-几何不等式推广为关于两组正数的改进型加权算术-几何不等式,其思路可为部分已有结论提供新的证明方法.突破关于自然对数的加权算术-几何不等式对具体函数的依赖,给出并证明了关于对数凸函数的加权算术-几何不等式.

The weighted arithmetic-geometric mean inequality for one group of positive numbers is generalized to suit for two groups of positive numbers,and our approach can be used to prove some correlate theorems.Another weighted arithmetic-geometric mean inequality about logarithmic convex functions is shown also.