Some Monotonicity Results for the Ratio of Two-Parameter Symmetric Homogeneous Functions

摘要

Applying well properties of homogeneous functions,some monotonicity results for the ratio of two-parameter symmetric homogeneous functions are presented, which give an easier access to find two-parameter symmetric homogeneous means having ratio simple monotonicity properties proposed by L. Losonczi. As an application, a chain of inequalities of ratio of bivariate means is established.