Correction to: On the fundamental triangle inequality and Gerretsen’s double inequality

On the metric triangle inequality

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

The Best Constants for a Double Inequality in a Triangle

In this short note, by using some of Chen’s theorems and classic analysis, we obtain a double inequality for triangle and give a positive answer to a problem posed by Yang and Yin [6].

Using the Triangle Inequality to Accelerate -Means

The -means algorithm is by far the most widely used method for discovering clusters in data. We show how to accelerate it dramatically, while still always computing exactly the same result as the standard algorithm. The accelerated algorithm avoids unnecessary distance calculations by applying the triangle inequality in two different ways, and by keeping track of lower and upper bounds for dist...

Triangle inequality for resistances

Given an electrical circuit each edge e of which is an isotropic conductor with a monomial conductivity function y∗ e = y r e/μ s e. In this formula, ye is the potential difference and y∗ e current in e, while μe is the resistance of e, while r and s are two strictly positive real parameters common for all edges. In 1987, Gvishiani and Gurvich [4] proved that, for every two nodes a, b of the ci...

The Poverty-Growth-Inequality Triangle