We are concerned with a well-known characterization of the Shannon entropy by Faddeev, suitably re-examined in the frame of Ulam-Hyers "stability" of functional equations. By use of some results about number theoretical functions, we give a sufficient condition that the solutions of a suitable system of countably many functional inequalities approximate the Shannon entropy uniformly.
A stability result concerning the Shannon entropy
MORANDO, Alessandro
2001-01-01
Abstract
We are concerned with a well-known characterization of the Shannon entropy by Faddeev, suitably re-examined in the frame of Ulam-Hyers "stability" of functional equations. By use of some results about number theoretical functions, we give a sufficient condition that the solutions of a suitable system of countably many functional inequalities approximate the Shannon entropy uniformly.File in questo prodotto:
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