On the symmetrized S -divergence

In this paper we worked with the relative divergence of type s , s ∈ ℝ, which include Kullback-Leibler divergence and the Hellinger and χ 2 distances as particular cases. We give here a study of the sym- metrized divergences in additive and multiplicative forms. Some ba-sic properties as symmetry, monotonicity and log-convexity are estab-lished. An important result from the Convexity Theory is also proved.