A New Method to Prove Several Inequalities

As is known to all, to strengthen and refine the famous arithmetic-geometric- harmonic mean inequality H (w, a) ≤ G (w, a) ≤ A (w, a), it has been becoming the focus of the theoretical research of inequality from estimating the mean difference. the difference between the two inequalities mentioned above is estimated by using variance, and these results are strengthened or generalized by using a consistent proof model.