广义Heron平均和幂平均的不等式

The Generalized Heron Meron Mean and Power Mean Inequalities

定出了使下式成立的最大P和最大小q其中b_1≥b_2>0,a_1/b_1≥a_2/b_1>0.

In this note, we determine the greatest p (=1/r) and the least value q (=(r+2)/(3r)) such that M_p(a_1, a_2)/M_p(b_1, b_2)≤I_r(a_1, a_2)/I_r(b_1, b_2)≤M_q(a_1, a_2)/M_q(b_1, b_2) is valid for b_1≥b_2>0, a_1/b_1≥a_2/b_2>0.