关于对称导数的几点注记

A Few Notes on Symmetric Derivative

本文主要讨论了对称导数的性质及用对称导数研究函数分析性质的一些理论和方法,进一步论证了对称导数与单调函数、凸函数的关系,得出了用对称导数判定函数单调性、凹凸性的三个比较简单的方法和凸函数的一个新定义。

This paper has focused on the discussion of the properties of symmetric derivative,some theories,and methods in studying the analytic properties of function us-ing symmetric derivative It explored the relation between symmetric deivative and con-vex function and monotone function It concluded with three simple methods in determin-ing the monotonicity, convexity of functions as well as a new definition of convex func-tion.