数学杂志2020，Vol.40Issue(1)：20-28,9.
算术-调和平均不等式的改进
IMPROVE INEQUALITIES OF ARITHMETIC-HARMONIC MEAN
摘要
Abstract
We study the refinement of arithmetic-harmonic mean inequalities.First,through the classical analysis method,the scalar inequalities are obtained,and then extended to the operator cases.Specifically,we have the following main results:for 0 ＜ v,τ ＜ 1,a,b ＞ 0 with (b-a)(τ-v) ＞ 0,we have a▽vb-a!vb/a▽τb-a!τb ≤ τ(1-τ)/τ(1-τ) and (a▽vb)2-(a!vb)2/(a▽τb)2-(a!τb)2 ≤v(1-v)/τ(1-τ),which are generalizations of the results of W.Liao et al.关键词
算术-调和平均/算子不等式/Hilbert-Schmidt范数Key words
arithmetic-harmonic mean/operator inequality/Hilbert-Schmidt norm分类
数理科学引用本文复制引用
杨长森,任永辉,张海霞..算术-调和平均不等式的改进[J].数学杂志,2020,40(1):20-28,9.基金项目
Supported by National Natural Science Foundation of China (11271112 （）
11771126 （）
11701154). （）
