可导函数的一致连续性判别

Decision methods of uniform continuity of derivable function

函数的一致连续性是一个重要的数学概念,关于函数一致连续性的判别通常是利用定义、Cantor定理及函数在区间端点的极限是否存在等方法,适用范围窄.在常用的判别法基础上,通过对可导函数进行研究,给出了一系列判别可导函数一致连续性的判别定理,特别是建立了函数一致连续性的比较判别法,使很多比较复杂的函数通过与一致连续性已知的函数进行比较,就可以判别出是否一致连续,扩大了判别范围,填补了函数一致连续性理论上的空白.

Uniform continuity of function is an important mathematical concept. In general, the decision methods of function＇ s uniform continuity are made from the perspective of defi- nition, Cantor theorem, the possibility of functional limit at the interval endpoints, and so on, which has disadvantages in practice. Based on the general decision methods and through the study of derivable function, this paper presented a series of decision theorems of uniform continuity of derivable function. Especially, the comparability methods of function＇ s uniform continuity were established, which made it possible to distinguish the uniform continuity of complex function through comparing it with the uniform continuous function. This method not only enlarged the scale of distinguishing, but also filled the gap of the theory of function＇ s u- niform continuity.