一种双参数平均及其应用

The Two-parameter Mean and Its Application

为有效的研究平均值及其关系,给出了一种双参数平均的定义,利用这种双参数平均关于参数的单调性,导出了许多著名的平均和不等式,同时对这些不等式给予了很好的几何刻画.

For researching several average values and the relationship of them effectively, this paper gives the definition of a two-parameter mean. Taking advantage of the two-parameter mean＇s monotony on parameter, a series of well-known means and inequalities are deduced and geometrical interpretations of inequalities are also presented.