Sharp Power Mean Bounds for the One-Parameter Harmonic Mean

Author:

Chu Yu-Ming1,Wu Li-Min2,Song Ying-Qing1

Affiliation:

1. School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China

2. Department of Mathematics, Huzhou University, Huzhou 313000, China

Abstract

We present the best possible parametersα=α(r)andβ=β(r)such that the double inequalityMα(a,b)<Hr(a,b)<Mβ(a,b)holds for allr(0,1/2)anda,b>0withab, whereMp(a,b)=[(ap+bp)/2]1/p  (p0)andM0(a,b)=abandHr(a,b)=2[ra+(1-r)b][rb+(1-r)a]/(a+b)are the power and one-parameter harmonic means ofaandb, respectively.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Analysis

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Optimal bounds for two Sándor-type means in terms of power means;Journal of Inequalities and Applications;2016-02-16

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