ScholarLens Back to search
2010•Journal of Inequalities and ApplicationsOpen access

Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means

Bo-Yong Long, Yu‐Ming Chu

Open full text 33 citations

Abstract

For , the generalized logarithmic mean , arithmetic mean , and geometric mean of two positive numbers and are defined by , for , , for , , and , , for , and , , for , and , , and , respectively. In this paper, we find the greatest value (or least value , resp.) such that the inequality (or , resp.) holds for (or , resp.) and all with .

Open-access reader

About this research paper

What this paper is about

For , the generalized logarithmic mean , arithmetic mean , and geometric mean of two positive numbers and are defined by , for , , for , , and , , for , and , , for , and , , and , respectively. In this paper, we find the greatest value (or least value , resp.) such that the inequality (or , resp.) holds for (or , resp.) and all with .

Why it matters

OpenAlex reports 33 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

For , the generalized logarithmic mean , arithmetic mean , and geometric mean of two positive numbers and are defined by , for , , for , , and , , for , and , , for , and , , and , respectively. In this paper, we find the greatest value (or least value , resp.) such that the inequality (or , resp.) holds for (or , resp.) and all with .

Key concepts: Mathematics, Logarithmic mean, Logarithm, Geometric mean, Inequality of arithmetic and geometric means, Mean value, Inequality, Value (mathematics)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means — Research Paper | ScholarLens