On the convexity of some divergence measures based on entropy functions

Three measures of divergence between vectors in a convex set of a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -dimensional real vector space are defined in terms of certain types of entropy functions, and their convexity property is studied. Among other results, a classification of the entropies of degree <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</tex> is obtained by the convexity of these measures. These results have applications in information theory and biological studies.