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Start Over Coverage 133-149

2. Optimal sublinear inequalities involving geometric and power means

Creator:
Wen, Jiajin, Cheng, Sui Sun, and Gao, Chaobang
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
geometric mean, power mean, Hermitian matrix, permanent of a complex, simplex, and arithmetic-geometric inequality
Language:
English
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public