关于两个凸函数乘积的不等式

Inequalities on Product of Two Convex Functions

针对两个正的连续凸函数,利用各自的算术平均值,给出它们乘积的算术平均值的上界.在这两个凸函数成似序时,这个上界比由Hermite-Hadamard不等式得到的上界要小.在这两个凸函数成反序时,这个上界与由Chebyshev不等式得到的上界各有强弱.

For two positive continuous convex functions, an upper bound of the arithmetic mean of their product is given by means of their respective arithmetic means. When these two convex functions are in similar order, the upper bound obtained is smaller than that obtained by Hermite-Hadamard inequality. When they are in opposite order, the upper bound obtained may be bigger or smaller than that obtained by Chebyshev inequality.