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The fundamental equation of information on open domain. (English) Zbl 0618.94004
The authors present the general solution of the fundamental equation of information \[ (1)\quad f(x)+(1-x)f(y/(1-x))=f(y)+(1-y)f(y/(1-y)) \] on the so-called ”open domain”, where f:(0,1)\(\to {\mathbb{R}}\) and (1) is valid for all \((x,y)\in D_ 0=\{(a,b):\) \(a,b,a+b\in (0,1)\}\). (Note that the extreme points 0 and 1 are not included in the domain.)
This result was recently generalized by a common paper of B. R. Ebanks, P. Kannappan and C. T. Ng [Aequationes Math. 32, 19-31 (1987; Zbl 0612.39006)].
Reviewer: W.Sander

MSC:
94A17 Measures of information, entropy
39B99 Functional equations and inequalities
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