与AM凸函数有关的积分不等式和单调函数

Integral inequalities and monotone functions related to AM-convex functions

利用凸函数与AM凸函数的关系,证明了AM凸函数存在单侧导数,并通过不等式建立了AM凸函数与其单侧导数的联系.在此基础上,用普通数学分析的方法获得了若干AM凸函数的不等式和单调函数.

With the aid of relationship between convex functions and AM -convex functions, the existence of unilateral derivatives of AM -convex functions is proved, and the relation between AM - convex function and its unilateral derivative is established through inequalities. Based on this groundwork, integral inequalities and monotone functions for AM- convex functions are obtained by using mathematical analysis.