Some Monotonicity Results for the Ratio ofTwo-Parameter Symmetric Homogeneous Functions

摘要

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