Optimal sublinear inequalities involving geometric and power means

Title:

Optimal sublinear inequalities involving geometric and power means

Creator:

Wen, Jiajin, Cheng, Sui Sun, and Gao, Chaobang

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6a3ffd6c-cb8d-43ce-be70-a9eb3e1a590b
uuid:6a3ffd6c-cb8d-43ce-be70-a9eb3e1a590b
doi:10.21136/MB.2009.140649

Subject:

geometric mean, power mean, Hermitian matrix, permanent of a complex, simplex, and arithmetic-geometric inequality

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

There are many relations involving the geometric means Gn(x) and power means [An(x γ )]1/γ for positive n-vectors x. Some of them assume the form of inequalities involving parameters. There then is the question of sharpness, which is quite difficult in general. In this paper we are concerned with inequalities of the form (1 − λ)G γ n(x) + λAγ n(x) ≥ An(x γ ) and (1 − λ)G γ n(x) + λAγ n(x) ≤ An(x γ ) with parameters λ ∈ R and γ ∈ (0, 1). We obtain a necessary and sufficient condition for the former inequality, and a sharp condition for the latter. Several applications of our results are also demonstrated.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

133-149

Source:

Mathematica bohemica | 2009 Volume:134 | Number:2

Harvested from:

CDK

Metadata only:

false