A Monotonicity Property of Ratios of Symmetric Homogeneous Means

摘要

We study a certain monotonicity property of ratios of means, which we call a strong inequality. These strong inequalities were recently shown to be related to the so-called relative metric. We also use the strong inequalities to derive new ordinary inequalities. The means studied are the extended mean value of Stolarsky, Gini's mean and Seiffert's mean.