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Recent results on the stability of the parametric fundamental equation of information. (English) Zbl 1224.39043
Summary: The purpose of this paper is to summarize the recent results on the stability of the parametric fundamental equation of information. Furthermore, by the help of a modification of a method we used in [E. Gselmann and G. Maksa, Aequationes Math. 78, No. 3, 271–282 (2009; Zbl 1207.39042)], we give a unified proof for the Hyers-Ulam stability of the equation in question, assuming that the parameter does not equal to 1. As a corollary of the main result, a system of equations, that defines the recursive and semi-symmetric information measures is also discussed.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
94A17 Measures of information, entropy
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