Geodesic
Remarks on the Entropy Equation
In the paper [4] A. Kamicute{n}ski and J. Mikusicute{n}ski have proved the following Theorem: If a function $H(x,y,z)$ is continuous, symmetric and positively homogeneous (of order 1) in the domain $D={(x,y,z)|x,y,z\geq 0, xy+yz+zx>0}$ and satisfied in the order of $D$ the functional equation $H(x,y,z)=H(x+y,0,z)+H(x,y,0)$ then $H(x,y,z)=c[(x+y+z)n(x+y+z)-xn x-yn y= zn z],$ where $c$ is a real constant and $0\ln 0=0$ 
@article{ZR_1976_1_9_a4,
     author = {Z. Dar\'oczy},
     title = {Remarks on the {Entropy} {Equation}},
     journal = {Zbornik radova},
     pages = {31 },
     publisher = {mathdoc},
     volume = {1},
     number = {9},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZR_1976_1_9_a4/}
}
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Z. Daróczy. Remarks on the Entropy Equation. Zbornik radova, Tome 1 (1976) no. 9, p. 31 . http://geodesic.mathdoc.fr/item/ZR_1976_1_9_a4/