Stability of the parametric fundamental equation of information for nonpositive parameters

TL;DR

This paper proves the stability of the parametric fundamental equation of information for nonpositive parameters, ensuring the robustness of related information measures under small perturbations.

Contribution

It establishes the stability of the fundamental equation of information for nonpositive parameters, extending the understanding of information measure stability.

Findings

Stability of the fundamental equation of information for nonpositive parameters.

Stability of recursive and semi-symmetric information measures.

Provides a stability framework for information measures depending on nonpositive parameters.

Abstract

In this note we prove that the parametric fundamental equation of information is stable in the sense of Hyers and Ulam provided that the parameter is nonpositive. We also prove, as a corollary, that the system of equations that defines the recursive and semi-symmetric information measures depending on a nonpositive parameter is stable in a certain sense.