Stability of the parametric fundamental equation of information for nonpositive parameters
arXiv:1307.0656 · doi:10.1007/s00010-009-2980-z
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.
10 pages, published in Aequationes Mathematicae in 2009