Bregman and Burbea-Rao divergence for matrices

Sa？etak In this paper, the Bregman and Burbea-Rao divergences for matrices are investigated. Two mean-value theorems for the divergences induced by C^2-functions are derived. As application, certain Cauchy type means of the entries of the matrices are constructed. By utilizing three classes of parametrized convex functions, the exponential convexity of the divergences, thought as a function of the parameter, is proved. The monotonicity of the corresponding means of Cauchy type is shown. Power means are also considered