中文摘要：

集值映射的导数形式众多，常见的如相依导数、相邻导数、约切导数，给出了一个满足合理假设的集值映射，借助该映射探究了集值映射上述三种导数的一致性，并利用该假设得到“preinvex映射必是伪凸映射”的简单证明。

英文摘要：

The derivative of set valued mapping there are many forms,common as the contingent derivative,the adjavative derivative,and the circatangent derivative.In this paper, A set valued mapping satisfying the reasonable assumption is given,by it,we discuss the consensus of three derivatives mentioned before,and obtain the simple proof of ＂the preinvex map is a pseudo con- vex map＂.