The general solution of a functional equation arising in information theory
type: Item
instance of: scholarly article
title: The general solution of a functional equation arising in information theory
zbMATH Open document ID: 0612.39007
DOI: 10.1007/BF01956325
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: The author gives all solutions of the functional equation \[ f(pq)+f(p(1- q))=f(p)(f(q)+f(1-q)) \] where p,q\(\in [0,1]\) and f is the unknown function f:[0,1]\(\to R\). The solutions are determined by showing that they can be expressed by the solution of the fundamental Cauchy equations \(f(xy)=f(x)f(y),\) x,y\(\in [0,1]\) and \(f(x+y)=f(x)+f(y),\) x,y\(\in R\).
Mathematics Subject Classification ID: 39B99
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 3989993
zbMATH Keywords: fundamental equation
zbMATH Keywords: information measures
zbMATH Keywords: Cauchy equations
author: Gyula Maksa
MaRDI profile type: Publication
cites work: Q5563736
cites work: On some functional equations of the information theory
full work available at URL: https://doi.org/10.1007/bf01956325
OpenAlex ID: W2087102999
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description: scientific article; zbMATH DE number 3989993