一类函数列积分中值点像点的单调性

Monotonicity of the image sequence about integral mean value points of a function sequence

探讨闭区间上非负连续函数列{g(x)fn(x)}积分中值点xn所产生的数列{f(xn)}的单调性,以及序列{fn(xn)}的收敛性,从而将与积分∫bag(x)fn(x)dx有关的积分极限问题转化为数列极限来解决.

This paper discusses the monotonicity of the sequence{f（xn）}generated by the integral mean value point of nonnegative continuous function sequence {g（x）fn（x）}on a closed interval,and then studies the convergence of the sequence {fn（xn）}.Furthermore,the integral limits about integral ∫bag（x）fn（x）dx are translated into sequence limits to solve it.