Reverse arithmetic-harmonic mean and mixed mean operator inequalities

Journal of inequalities and applications

Wenshi Liao¹ 

关键词: arithmetic-harmonic mean;    mixed mean;    Kantorovich constant;    operator inequalities;    47A63;    47A64;    47C15;   

DOI  :  10.1186/s13660-015-0735-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This note aims to present some scalar inequalities and operator inequalities on a Hilbert space. Firstly, the direct reverse weighted arithmetic-harmonic mean inequalities for scalars are obtained. Secondly, based on these scalar inequalities, the corresponding operator inequalities are established. Finally, we present the mixed arithmetic-geometric and geometric-harmonic means inequalities for two positive operators.

【 授权许可】

CC BY