应用凸函数证明不等式的2点注记

Two Notes on Proving Inequation by Using Convex Function

基于凸函数的判别定理,指出了在应用凸函数证明不等式时应注意的问题,即二阶导数是否存在决定了利用凸函数证明不等式的出发点.之后,应用凸函数的性质证明了康托洛维奇不等式的矩阵形式.

Based on the distinguishing theorem for convex function, the author indicates some problems needing attention on proving inequation by using convex function.whether there exists second derivative is the starting point in proving some inequation. The author then proves the matrix form of Kantorovich inequation by using the property of convex function.