On the modified entropy equation

Abstract

The object of this paper is to solve the so--called modified entropy equation \[ f<x, y, z>=f<x, y+z, \mathbf{0}>+ μ<y+z>f<\mathbf{0}, \frac{y}{y+z}, \frac{z}{y+z}>, \] 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.

19 pages http://www.emis.de/journals/BJMA/tex_v2_n1_a12.pdf, published in Banach Journal of Mathematics in 2008