齐次可微函数的对角递减性与一类不等式的证明  

The diagonal decreasing property of homogeneous differentiable functions and the proof of a class of inequalities

作　　者：姚勇[1] 王挽澜[2] 秦小林[1] YAO Yong;WANG Wan-lan;QIN Xiao-lin(Chengdu Institute of Computer Application,Chinese Academy Sciences,Chengdu 610041,China;School of Information Sciences and Technology,Chengdu University,Chengdu 610106,China)

机构地区：[1]中国科学院成都计算机应用研究所,四川成都610041 [2]成都大学信息科学与技术学院,四川成都610106

出　　处：《西南民族大学学报（自然科学版）》2020年第5期542-550,共9页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：中科院西部青年学者项目(201899);四川省科技计划资助项目(2018GZDZX0041)。

摘　　要：研究了齐次可微函数的对角递减性.对角递减性可以被使用去证明许多不等式,如算术-几何(A-G)平均不等式, Schur不等式, Suranyi不等式等等.文中计算出了对角递减函数在非负三元二次型中出现的概率约为57%.为了弥补对角递减性的不足引入了分块对角递减性的概念.证明了在标准单形上严格正的齐次多项式都是分块对角递减函数.The diagonal decreasing property of homogeneous differentiable functions(DDF)is investigated in this article.It can be used to prove many inequalities,such as arithmetic geometric(A-G)mean inequality,Schur inequality,and Suranyi inequality.According to the calculation in this paper,the probability of occurrence of diagonal decreasing function in nonnegative ternary quadratic form is about 57%.In order to make up for the deficiency of diagonal decreasing,the concept of block diagonal decreasing is introduced.It is proved that strictly positive homogeneous polynomials on a standard simplex are block diagonal decreasing functions.

关 键 词：齐次可微函数 对角递减函数 不等式 

分 类 号：O178[理学—数学]