关于L与G和A的加权算术平均不等式

THE INEQUALITY BETWEEN THE UNWEIGTED LOGARITHMIC MEAN L AND THE WEIGHTED ARITHMETIC MEAN OF G AND A

利用函数的单调性来研究对数平均L(a,b)与几何平均G(a,b)和算术平均A(a,b)的加权算术平均之间的关系,从而拓广了不等式理论的研究范围。

The logarithmic mean L(a,b)is compared with the weighted arithmetic mean of the geometric mean G(a,b)and the arithmetic mean A(a,b)by the monotonity of a function,then the regions of the inequalities is developed.