摘要
首先利用凸函数与HA-凸函数的关系证明了HA-凸函数存在单侧导数,并通过不等式给出HA-凸函数与其单侧导数的联系.然后给出HA-凸函数的一个充要条件和一个积分性质.利用以上结果,得到HA-凸函数的若干积分不等式.
With the aid of relationship between convex functions and HA-convex functions, the existence of unilateral derivatives of HA-convex functions is firstly proved, and the relation between HA-convex functions and its unilateral derivative is established through inequalities. Then a sufficient and necessary condition and an integral property for HA-convex functions are given. Finally, using the above results, some integral inequalities for HA-convex functions are obtained.
出处
《湖南理工学院学报（自然科学版）》
CAS
2015年第4期1-5,36,共6页
Journal of Hunan Institute of Science and Technology(Natural Sciences)
关键词
HA-凸函数
积分不等式
单侧导数
HA-convex function
integral inequality
unilateral derivative
