舒尔几何凸函数与一类条件不等式  

Schur-geometrically convex function and a class of conditional inequalities

作　　者：石焕南[1] 王东生[2] SHI Huannan;WANG Dongsheng(Teacher’s College,Beijing Union University,Beijing 100011;Basic courses department,Beijing Vocational College of Electronic Technology,Beijing 100176)

机构地区：[1]北京联合大学师范学院,北京100011 [2]北京电子科技职业学院基础部,北京100176

出　　处：《首都师范大学学报（自然科学版）》2022年第5期16-20,76,共6页Journal of Capital Normal University：Natural Science Edition

摘　　要：受控理论是一门新兴数学学科,舒尔(Schur)凸函数是其核心概念,舒尔几何凸函数是舒尔凸函数的推广.变量乘积为定值的条件不等式是一类常见的不等式,本文利用舒尔几何凸函数证明了10个此类不等式,方法别样、简洁、有趣,还得到一些加强的结果 .Majorization theory is a new mathematical subject,Schur convex function is its core concept,and Schur geometrically convex function is the generalization of Schur convex function. The conditional inequalities in which the product of variables is constant are a common class of inequalities.In this paper,ten such inequalities are proved by Schur geometrically convex function. The method is different,concise and interesting,and some strengthened results are obtained.

关 键 词：舒尔几何凸函数 受控 条件不等式 

分 类 号：O178[理学—数学]