指数均值、对数均值与幂均值的序关系

The Sequential Relationship among Mean Value of Index, Mean Value of Logarithm and Mean Value of Power

自1957年Ostle和Terwilliger发现不等式以来,指数均值、对数均值和幂均值之间的序关系引起了不少学者的兴趣.1983年,徐利治教授用分析方法证明了林同坡不等式和Stolarsky不等式.利用徐利治教授的分析方法和无穷小技术,对指数均值、对数均值和幂均值之间的序关系进行系统讨论,得出了一些有意义的结果.

Since Ostle and Terwilliger discovered the inequality in 1957, the sequential relationship among mean value of index, mean value of logarithm and mean value of power has aroused great interests of many scholars, for example, the inequality in the first to the ninth reference books. In 1983, Professor Xu Lizhi proved the inequality of Lin Tongpo and Stolarsky by analytical method in the third reference book. By applying the analytical method used by Professor Xu and infinitely small skill, the writers discuss systematically the sequential relationship among mean value of index, mean value of logarithm and mean value of power and obtains some meaningful results.