给出一种新的Sylvester型泛函A(K)的定义.运用影子系统,研究A(K)的极值问题.当K为椭球时，A(K)取得最小值.在平面上,当K为三角形时，A(K)取得最大值.对称情形的极值凸体为平行四边形.

This paper defines a new Sylvester type functional A(K). Using the method of shadow systems, the extremal problems of A(K) are studied. When K is a ellipsoid, A(K) attains its minimum value. In a plane, A(K) attains its maximum value when Kis a triangle. When K is symmetric, the corresponding example is parallelogram. 