Banach Journal of Mathematical Analysis

On the modified entropy equation

Eszter Gselmann

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336277

Digital Object Identifier
doi:10.15352/bjma/1240336277

Mathematical Reviews number (MathSciNet)
MR2404713

Zentralblatt MATH identifier
1152.39019

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

Keywords
entropy, entropy equation fundamental equation of information associativity equation

Citation

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


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References

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