关于一类凸函数的对称平均

On a Symmetric Mean of Convex Function

定义了一类凸函数的对称平均，建立了其基本定理，推广了 Ｆａｎｋｙ不等式和 Ｊｅｎｓｅｎ不等式．最后证明了第二ｋ次和第三ｋ次对称平均，说明基本定理的应用。

The author defines a symmetric mean of convex function and sets up its basic inequality. He also generalizes 'Fanky inequality' and Jensen inequality' by means of the basic inequality. And finally, the second korder symmetric mean and the third k-order symmetric mean are proved there.