TL;DR
This paper proves the hyperstability of the parametric fundamental equation of information for negative parameters and demonstrates the stability of alpha-recursive information measures.
Contribution
It establishes hyperstability results for a key information equation and its related systems, extending stability theory in information measures.
Findings
The parametric fundamental equation of information is hyperstable for negative parameters.
The system defining alpha-recursive information measures is stable.
Stability holds on both open and closed domains.
Abstract
The aim of this paper is to prove that the parametric fundamental equation of information is hyperstable on its open as well as on its closed domain, assuming that the parameter is negative. As a corollary of the main result, it is also proved that the system of equation that defines the alpha-recursive information measures is stable.
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