一个加权的Kantorovich不等式及其应用

A Weighted Kantorovich's Inequality and its Application

在研究离散型和积分型Kantorovich不等式的基础上,通过归纳类比的方法,得到了新的Kantorovich不等式的加权推广积分形式,并运用构造性方法给出了一种简洁有趣的证明.又进一步从新的Kantorovich加权积分不等式推出了Pólya-Szeg加权积分不等式,最后指出了Kantorovich加权积分不等式与Buniakowski-Cauchy-Schwarz加权积分不等式的关系,以彰显其内在规律性和应用性.

On the basis of studying of the discrete and integral Kantorovich inequality as well as the induction analogy method, a simple and new weighted popularization of Kantorovich＇ s integral inequality was obtained. An easy and interesting constructive demonstration was given. A weighed integral inequality of Pólya-Szegoefrom a new weighed integral inequality of Kantorovich was also deduced. Finally, the relation between Kantorovich＇s weighted integral inequality and Buniakowski-Cauchy-Schwarz＇ s weighted integral inequality was put forward in order to reflect its inner regularity and application.