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Stability of the parametric fundamental equation of information for nonpositive parameters

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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.

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Correspondence to Eszter Gselmann.

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Manuscript received: February 18, 2008 and, in final form, July 11, 2008.

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Gselmann, E., Maksa, G. Stability of the parametric fundamental equation of information for nonpositive parameters. Aequat. Math. 78, 271 (2009). https://doi.org/10.1007/s00010-009-2980-z

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  • DOI: https://doi.org/10.1007/s00010-009-2980-z

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