关于平均值不等式的加强

The Sharpening of Mean-value Inequality

对文［１］提出的平均值不等式（１）这里α＝（１—１／ｎ）ｒ－１，１≤ｒ≤ｎ，用Ｓｃｈｕｒ─凸性理论证明对于α＝（ｒ２－ｒ十１）／ｒ２，ｒ≥１时（１）及其对应的积分不等式都成立。

In this poper,the following results are proved by means of the theory of mojorhation.Propeitionl Let x , and α= (r2-r+1 )/r2,Then There is sttict inequality unless The analogous continuotis veraion also holds(see the inequality(4) in Propedon 2).Another unpubliShed and inter￣g problem posed by Chen Ji is the following:'Can we find a least value a such that the inequality(1) holds?