函数的双参数平均的几个性质

Some Properties for Two-Parameter Mean of Function

对于函数 f(x) q的双参数平均 Mp,q(f;a,b) ,证明当 f(x)为单调函数时它是 a,b的单调函数 ;当f (x)不是常量时它是 p。

For two-parameter mean of function M p,q (f;a,b), the deserfation tries to prove that it is the mon otone function of a and b when f(x) is the same; while it is the str ictly monotone increasing function of p and q when f(x) is not const ant.