Stability type results concerning the fundamental equation of information of multiplicative type

TL;DR

This paper investigates the stability of the fundamental equation of information of multiplicative type, proving Hyers-Ulam stability and applying it to recursive measures of information.

Contribution

It establishes the Hyers-Ulam stability of the fundamental equation of information of multiplicative type, a novel result in the field.

Findings

The fundamental equation of information of multiplicative type is stable under certain conditions.

Stability results are applied to recursive measures of information.

The paper extends stability analysis to a system of related functional equations.

Abstract

The paper deals with the stability of the fundamental equation of information of multiplicative type. It will be proved that the equation in question is stable in the sense of Hyers and Ulam under some assumptions. This result will be applied to prove the stability of a system of functional equations that characterizes the recursive measures of information of multiplicative type.