凸函数和凹函数的幂平均不等式

The Mean Value Inequality of the Power about the Convex Function and Concave Function

文 [1 ]获得了当 α≥ 1时的凸函数的幂平均不等式 (3)、(4 ) [1] .本文指出文 [1 ]中的一个错误 ,并且得到了 α≤ 1时的凹函数的幂平均不等式 .修正和充实了文 [1 ]的定理 .同时讨论了当 α取其它值时不等式的情况 .

The mean value inequality of the power about the convex function (3)\,(4) [1] has been obtained when α≥1 in paper \. This paper points out an error in paper \, It is in this paper that the author obtains the mean value inequality of power about the concave function when α≤1, corrects and enriches the theorem in paper \, and also discusses the mean value inequality of the power in other cases of α.