建立不等式的降维方法(Ⅰ)

The method of descending dimension for establishing inequalities (I)

使用一种称为降维法的新方法建立一些著名不等式,包含算术平均-几何平均不等式、马克劳林不等式、切比雪夫不等式和琴生不等式.通过这些论证可以看出,这种新近发展的方法在建立不等式的研究中能够广泛地应用.也可以看出,此种方法有别于另外一些归纳技巧.

We use a new method that is called the method of descending dimension to establish some well-known inequalities, including the arithmetic mean-geometric mean, Maclaurin's, Cebysev's and Jensen's inequalities. Via these arguments, we can observe that the newly developed method is widely used in studies of establishing inequalities. We can also observe that the method is constructed in a form somewhat differing from that of other technique of induction used for proving inequalities.