Banach Journal of Mathematical Analysis

On the modified entropy equation

Eszter Gselmann

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The object of this paper is to solve the so--called modified entropy equation \[ f\left(x, y, z\right)=f\left(x, y+z, \mathbf{0}\right)+ \mu\left(y+z\right)f\left(\mathbf{0}, \frac{y}{y+z}, \frac{z}{y+z}\right), \] on the positive cone of ${\mathbb R}^{k}$, where $\mu$ is a given multiplicative function on this cone. After that the regular solutions of this equation are determined. Furthermore we investigate its connection between the entropy equation and other equations, as well.

Article information

Banach J. Math. Anal., Volume 2, Number 1 (2008), 84-96.

First available in Project Euclid: 21 April 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39B40
Secondary: 94A17: Measures of information, entropy

entropy, entropy equation fundamental equation of information associativity equation


Gselmann, Eszter. On the modified entropy equation. Banach J. Math. Anal. 2 (2008), no. 1, 84--96. doi:10.15352/bjma/1240336277.

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