On a Generalized Fundamental Equation of Information

Kannappan, Pl. ; Ng, C. T.

Canadian journal of mathematics, Tome 35 (1983) no. 5, pp. 862-872

Résumé

The object of this paper is to determine the general solution of the functional equation FE where α is multiplicative. It turns out that non-trivial embeddings of the reals in the complex generate some interesting solutions.In many applications, various special cases of (FE) have occurred ([1,3, 4, 6, 10, 11, 14]). The special case where f = g = h = k and α = the identity map is known as the fundamental equation of information, and has been extensively investigated by many authors ([5]). The case where f = g = h = k and α is multiplicative was treated in [13, 14]. The general solution of (FE) when α(1 – x) = (1 – x)β has been obtained in [9], except when β = 2.

Détail

DOI : 10.4153/CJM-1983-049-1

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