A New Proof of the Arithmetic—The Geometric Mean Inequality

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...

Improved logarithmic-geometric mean inequality and its application

In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.

The matrix arithmetic-geometric mean inequality revisited

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...

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.