Entropy functions and functional equations

TL;DR

This paper provides the general solutions to functional equations related to Shannon and Tsallis entropies, showing that previous regularity assumptions can be significantly relaxed, thus broadening the understanding of these entropy functions.

Contribution

It offers the complete solutions to key functional equations for Shannon and Tsallis entropies, extending prior results by weakening regularity conditions.

Findings

General solutions to entropy-related functional equations

Regular solutions under weaker assumptions

Broader applicability of entropy functional equations

Abstract

The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well. Furthermore, we point out that the regularity assumptions used in previous works can substantially be weakened.