Young不等式、Holder不等式与Minkowski不等式的新证法

A New Proof of Young's, H(o|¨)lder's and Minkowski's Inequalities

本文给出著名的Young不等式,H(?)lder不等式与Minkowski不等式的新证法。在通常的书上都利用Young不等式来证H(?)lder不等式,再用H(?)lder不等式来证Minkowski不等式。而在本文中用凸函数的特性证明上述三个不等式。

This paper gives a new proof of the famous Young's, Holder's and Minkow-ski's inequalities. In the ordinary books, the Holder's inequality is usually the developed by making use of the young's inequality, the Minkowski's inequality is developed by making use of the Holder's inequality. In this paper, however, proof of the above three inequalities are derived by means of the property of a convex function.