几类广义凸函数的等价刻画  

Equivalent Characterizations of Several Classes of Generalized Convex Functions

作　　者：韩淑霞[1] 韩志斌[1] 黄永忠[1] HAN Shuxia;HAN Zhibin;HUANG Yongzhong(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学数学与统计学院,武汉430074

出　　处：《大学数学》2022年第5期67-73,共7页College Mathematics

基　　金：高等学校大学数学教学研究与发展中心2020教学教改项目(CMC20200204);华中科技大学教学研究专项项目(2019026)。

摘　　要：通过介绍调和算术凸函数和几何算术凸函数的等价刻画,给出了几类广义凸函数的等价刻画.这些等价刻画是用广义凸函数与某种初等函数复合或者四则运算所得函数的经典凸性来实现的,从而丰富了各种广义凸函数的判别手段,降低了各种广义凸函数判别的难度.最后通过几个广义凸函数判别的例子进一步加深对不同广义凸函数的理解.By introducing the equivalent characterizations of HA-convex and GA-convex functions,the equivalent characterizations for several kinds of generalized convex functions are given.These equivalent characterizations are achieved by the classical convexity of a function,which is a combination of a generalized convex function and an elementary function or by four operations.This greatly enriches the methods of distinguishing generalized convex function and reduces the difficulty of identifying generalized convex functions.Finally,several examples are given to further understand different generalized convex functions.

关 键 词：凸函数 广义凸函数 等价刻画 

分 类 号：O177.5[理学—数学]