A Proof of the Arithmetic Mean-Geometric Mean Inequality

The matrix arithmetic-geometric mean inequality revisited

A Relationship between Subpermanents and the Arithmetic-Geometric Mean Inequality

Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n × n matrices F. In the case k = n, we exhibit an n 2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries.

An Alternative and United Proof of a Double Inequality for Bounding the Arithmetic-geometric Mean

For more information on the arithmetic-geometric mean and the complete elliptic integral of the first kind, please refer to [2, pp. 132–136], [4] and related references therein. In [4, Theorem 4] and [6], it was proved that the inequality M(a, b) ≥ L(a, b) (5) holds true for positive numbers a and b and that the inequality (5) becomes equality if and only if a = b, where L(a, b) = b− a ln b− ln...

Best Upper Bounds Based on the Arithmetic-geometric Mean Inequality

In this paper we obtain a best upper bound for the ratio of the extreme values of positive numbers in terms of the arithmetic-geometric means ratio. This has immediate consequences for condition numbers of matrices and the standard deviation of equiprobable events. It also allows for a refinement of Schwarz’s vector inequality.

Generalizing the Arithmetic Geometric Mean

The paper discusses the asymptotic behavior of generalizations of the Gauss’s arithmetic-geometric mean, associated with the names Meissel (1875) and Borchardt (1876). The "hapless computer experiment" in the title refers to the fact that the author at an earlier stage thought that one had genuine asymptotic formulae but it is now shown that in general "fluctuations" are present. However, no ve...