# General Inequalities

• Dragoslav S. Mitrinović
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 165)

## Abstract

Let a = (a1, ..., an) be a given sequence of positive numbers. Then the harmonic mean Hn (a) of the numbers a1, ..., an is defined as
$${{H}_{n}}(a)=\frac{n}{\frac{1}{{{a}_{1}}}+...+\frac{1}{{{a}_{n}}}};$$
their geometric mean Gn(a) is defined as
$${{G}_{n}}(a)={{({{a}_{1}} ... {{a}_{n}})}^{1/n}};$$
and their arithmetic mean An (a) is defined as
$${{\mathrm{A}}_{\mathrm{n}}}\mathrm{(a)=}\frac{{{\mathrm{a}}_{\mathrm{1}}}\mathrm{+}...\mathrm{+}{{\mathrm{a}}_{\mathrm{n}}}}{\mathrm{n}}$$
.

## Keywords

Integral Inequality Discrete Analogue Related Inequality Elementary Symmetric Function General Inequality
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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