Optimal Inequalities among Various Means of Two Arguments-Reference-Cited by-同舟云学术

Optimal Inequalities among Various Means of Two Arguments

Published:2009 Issue: Volume:2009 Page:1-10
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Shi Ming-yu¹,Chu Yu-ming²,Jiang Yue-ping¹

Affiliation:

1. College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

2. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Abstract

We establish two optimal inequalities among power meanMp(a,b)=(ap/2+bp/2)1/p, arithmetic meanA(a,b)=(a+b)/2, logarithmic meanL(a,b)=(a−b)/(log⁡a−log⁡b), and geometric meanG(a,b)=ab.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2009/694394.pdf

Reference18 articles.

1. Generalization and sharpness of the power means inequality and their applications

2. Sharp power mean bounds for the Gaussian hypergeometric function

3. Inequalities for Means in Two Variables

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