广义导数及其应用

为克服Clarke F．H．提出的局部Lipschitz函数的广义梯度，对一般的连续函数无法定义，以及在函数F（x）的可微点x0的广义梯度δF（x0）不一定和普通导数一致的局限，利用上、下极限的概念提出一种广义导数的概念，得到了广义导数的运算法则，以及连续函数的中值定理。这一概念和广义梯度一样具有许多良好的性质，且运算及证明都比较简单。

Generalized derivatives and its application

Devoted to overcoming the impossibility of defining common continuous functions by means of the generalized gradient of the partial Lipschitz functions, as put forward by F. H. Clarke, the uncertainty of the generalized gradient at differential point x0, and the limit of the consistency of general derivatives, the paper proposes the concept of generalized gradient in light of the concepts of limes inferiors and limes superiors and offers the rule of operation of the generalized function and the mean value theorem of the continuous function. This concept, like the generalized gradient, enjoys many good qualities and gives a more simple operation and proof.