华东师范大学学报（自然科学版）Issue(3)：46-54,120,10.DOI:10.3969/j.issn.1000-5641.2018.03.006
A(M)(s)-凸函数及其Jensen型不等式
A(M)(s)-Convex function and its Jensen-type inequality
摘要
Abstract
Based on the convexity and general convexity of a function,the authors study extending issues of a convex function.Firstly,the concept and sign of weighted r-th power s-mean of n positives are introduced;secondly,the A(M)(s)-convex function is defined by weighted r-th power s-mean;thirdly,the judgment theorem and operation properties of A(M)(s)-convex function are discussed;and finally,the Jensen-type inequality of the A(M)(s)-convex function is proved and an equivalent form is provided.The study shows that the A(M)(s)-convex function is a subset of general convex functions that includes many convex functions.Studying the A(M)(s)-convex function with the method of weighted r-th power s-mean is an effective way of extending and studying convex functions.This method explores a new approach to extending and studying convex functions.关键词
加权r次幂s-平均/A(M)(s)-凸函数/判定定理/运算性质/Jensen型不等式Key words
weighted r-th power s-mean/A(M)(s)-convex function/judgment theorem/operation property/Jensen-type inequality分类
数理科学引用本文复制引用
宋振云,胡付高..A(M)(s)-凸函数及其Jensen型不等式[J].华东师范大学学报（自然科学版）,2018,(3):46-54,120,10.基金项目
教育部科学技术研究重点项目(212109) （212109）
