Stability of the entropy equation

In this paper we prove that the so--called entropy equation, i.e., $H\left(x, y, z\right)=H\left(x+y, 0, z\right)+H\left(x, y, 0\right)$ is stable in the sense of Hyers and Ulam on the positive cone of $\mathbb{R}^{3}$, assuming that the function $H$ is approximatively symmetric in each variable and approximatively homogeneous of degree $α$, where $α$ is an arbitrarily fixed real number.

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