A characterization of the relative entropies

Abstract. In this note we give a characterization of a family of relative entropies on open domain depending on a real parameter \(\alpha\), which is based on recursivity and semisymmetry. In cases \(\alpha=1\) and \(\alpha=0\) we use a weak regularity assumption additionally while in the other cases no regularity assumptions are made at all.

Key words and phrases. Shannon relative entropy, Tsallis relative entropy, relative information measure, information function.