一类面积函数的最小值点的特性

The Characteristics of Minimum Point of Some Area Functions

本文运用Ｒｉｅｍａｎｎ－Ｓｔｉｅｌｊｅｏ积分的基本性质讨论了一类由连续单调函数所确定的面积函数的最小值问题，得到了该问题的最小值点恰为区问的中点。其变形问题的最小值点的函数值与函数在两端点的函数值的均值相等。

The minimum of some area functions is discussed by using Riemann-Stieljes integral. We achieved that the minimum point equals to the middle point of the interval discussed and in another case,the middle point equals to the point which satisfies: f(t)=(f(a)+f(b)).