一个完全对称函数的复合函数Schur凸性的简单证明  

A Simple Proof of Schur Convexity for a Composite Function of Complete Symmetric Function

作　　者：梁赛男 孙明保[1] 陈南博 LIANG Sainan;SUN Mingbao;CHEN Nanbo(School of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006,China;School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]湖南理工学院数学学院,湖南岳阳414006 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《湖南理工学院学报（自然科学版）》2023年第3期8-11,共4页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：湖南省教育厅科研项目(20A217,20C0905)。

摘　　要：针对一个完全对称函数的复合函数Schur凸性问题,基于Schur凸函数的性质给出了已有结果的又一证明.证明的主要思想方法是构造合适的复合函数,并利用复合函数的Schur凸性、Schur凸函数与Schur乘性凸函数或Schur调和凸函数的关系,给出了完全对称函数的复合函数Schur凸性、Schur乘性凸性和Schur调和性的简单证明.For the Schur convexity problem of a composite function of complete symmetric function,we gave another proof based on the properties of the Schur convex function.The main idea of the proof is to construct a suitable composite function,and using the Schur convexity of the composite function,the relationship between the Schur convex function and the Schur multiplicative convex function or the Schur harmonic convex function,we gave a simple proof of the Schur convexity,Schur multiplicative convexity and Schur harmonic convexity for the composite function of the complete symmetric function.

关 键 词：完全对称函数 Schur凸 Schur乘性凸 Schur调和凸 

分 类 号：O178[理学—数学]