**1. Introduction**

The *p*-norms in R<sup>3</sup> have applications in many branches of mathematics, physics and computer science. For *p* ≥ 1, the *p*-norm of the vector **x** = (*<sup>x</sup>*, *y*, *z*) ∈ R<sup>3</sup> (also called *Lp*-norm) is defined as

$$||\mathbf{x}||\_p = \left( |\mathbf{x}|^p + |y|^p + |z|^p \right)^{1/p} . \tag{1}$$

For *p* = 2, we arrive at the Euclidean norm, and when *p* → ∞ the norm is called the infinity norm or the maximum norm and is given by

$$\|\mathbf{x}\|\_{\infty} = \max(|\mathbf{x}|, |y|, |z|).$$

When *p* ∈ (0, <sup>1</sup>), Formula (1) does not define a norm, because the triangle inequality is not satisfied.
