On a bounded version of Holder's Theorem and an application to the permutability equation

TL;DR

This paper proves a representation theorem for the permutability equation using a bounded version of Holder's Theorem, with applications to various scientific and geometric laws.

Contribution

It introduces a bounded version of Holder's Theorem and applies it to generalize a representation theorem for the permutability equation.

Findings

Generalizes a known result for the permutability equation

Provides a bounded version of Holder's Theorem

Applicable to multiple scientific and geometric laws

Abstract

The permutability equation G(G(x,y),z) = G(G(x,z),y) is satisfied by many scientific and geometric laws. A few examples among many are: The Lorentz-FitzGerald Contraction, Beer's Law, the Pythagorean Theorem, and the formula for computing the volume of a cylinder. We prove here a representation theorem for the permutability equation, which generalizes a well-known result. The proof is based on a bounded version of Holder's Theorem.