建立不等式的拟单调函数方法与涉及幂平均的线性不等式问题  

Quasimonotone Function for Constructing Inequality and Problems of Linear Inequalities Involving Power Means

作　　者：文家金[1] 王挽澜[1] 

机构地区：[1]成都大学信息科学与技术学院,四川成都610106

出　　处：《成都大学学报（自然科学版）》2009年第2期112-118,共7页Journal of Chengdu University（Natural Science Edition）

基　　金：四川省教育厅自然科学重点项目资助(07ZA207)

摘　　要：提出建立高维解析不等式的拟单调函数方法.获得的主要结果是:在适当的假设下,如果涉及齐次对称函数的不等式问题可用优超理论或差分代换平凡非负方法处理,那么这类问题也能用拟单调函数方法处理.同时,用该方法处理了一类涉及幂平均的线性不等式问题.In order to establish a lot of analytical inequalities on high-dimensional space, a method of quasimonotone function was proposed. The main results are the following： with the proper hypotheses, if the problems of inequalities involving syrmnetric homogeneous functions can be settled via the theory of majorizations or the trivial non-negative of difference substitution, then these problems also can be settled by quasimonotone function method. For applications, several problems of linear inequalities involving power means are solved.

关 键 词：拟单调函数 Schur-凸函数 差分代换 幂平均 HERMITE矩阵 

分 类 号：O178[理学—数学]