收敛函数列的最小值及最小值点的一个性质

A Behavior of Minimal Value and Minimal Value Point on A Convergent Sequence of Funcitions

讨论了收敛函数列最小值及最小值点的极限性质 ,得到了在一定条件下 ,函数列最小值的极限等于其极限函数的最小值 。

In this paper, if given a sequence of functions {f n(x)} ,and there exists that lim n→∞ f n(x)=f(x), when imposed some conditions on this sequence {f n(x)} , then the sequence of points {x n} , which f n(x) attain its minimal value at x n , will converge to x 0 which is a minimal value point of f(x) , meanwhile, the sequence {m n} , which f n(x n) equals to m n will also converge to m which is a minimal value of f(x) .