浙江大学学报（理学版）2017，Vol.44Issue(4)：411-416,6.DOI:10.3785/j.issn.1008-9497.2017.04.004
MM-凸函数及其Jensen型不等式
MM-convex function & its Jensen-type inequality
摘要
Abstract
Considering the general convexity of functions, the authors present the definition of MM-convex function with two variables power means within the interval.Based on the definition, this article discusses its judgment theorems and operation properties, sets up its Jensen-type inequality, and provides the equivalent form of Jensen-type inequality and the deduction.Results show that MM-convex function is an extension of all convex functions determined by the power mean value of two arbitrary points within the definition domain of comparison function and by the power mean of the value.The introduction of MM-convex function brings an effective approach to deep study and further extension of convex function.关键词
凸函数/MM-凸函数/判定定理/运算性质/Jensen型不等式分类
数理科学引用本文复制引用
宋振云,陈少元,胡付高..MM-凸函数及其Jensen型不等式[J].浙江大学学报（理学版）,2017,44(4):411-416,6.基金项目
教育部科学技术研究重点项目(212109). （212109）
