线性空间上凸函数的若干判定定理

Some Decision Theories of Convex Function in Linear Spaces

文[1]给出了凸函数、严格凸函数、显凸函数的判别准则。本文对线性空间中的凸集上的实值函数定义一种导数,用其研究函数凸性,得到了上述三种凸函数的若干判定定理。

Some criteria of convex function,strictly convex function and explicitly convex function are given in [1]. This paper defines a kind of derivative for real function on convex set which is in linear space. By means of the derivative we study convexity of function and obtain some decision theories.