函数列与函数项级数的一致可导性

The Uniform Differentiability of the Sequence of Function and the Series of Function Item

运用函数的一致可导性与其导函数的一致连续性之间的关系,结合函数列的等度连续,探讨了函数列和函数项级数所确定的函数的一致可导性,并证明了一致可导函数列的极限函数(函数项级数和函数)的导函数与其导函数列的极限函数(导函数项级数的和函数)是一致的.

It reviews the relationship between the function's uniform differentiability and the uniform succession of its derivative,and the uniform succession of the sequence of function,in order to discuss two problems.The first problem is the uniform differentiability of the function determined by the sequence of function or the series of function item.Another,this paper proves the uniformity in the derivative of the limits of the sequence of function(the series of function item)and the limits of the sequence of derived function(the series of derived function item).