不动点定理在积分第一中值定理中的应用

Application of Fixed Point Theorem to First Integral Mean Value Theorem

利用不动点定理证明了积分第一中值定理的有关结论。在加强一个条件0<k<f′(x)<1的情况下,通过构造闭区间[a,b]上的一个压缩映照T(x),证明了积分第一中值定理中的ξ是唯一的。

Some results of the first integral mean value theorem were proved. With the additional condition of 0 〈 k 〈 f′ （ x ） 〈 1, it shows that the unique ξ satisfies the first integral mean value theorem by the contraction mapping T（x） on the [a,b].