Estimations of divergence measures for majorization inequalities via Peano’s representation of Hermite’s polynomial

Purpose In this paper applications to information theory are presented. Generalized majorization theorem is presented in term of different entropies and divergences. So that obtained results are generalized and comprehensive. Design/methodology/approach The analytical approach is used to prove the results. i.e. Different n-convex functions are used to prove results. Generalized majorization theorem and Peanos’s representation of Hermite polynomial are also imply. Findings The results related to Csiszár f divergence using generalized majorization theorem via Peanos’s representation of Hermite polynomial are proved. In seek of applications, generalized results are established using Shannon entropy, Kullback-Leibler distance. Moreover, the unique cases of obtained results are derived in terms of Bhattacharyya coefficient, Jeffrey’s distance and Triangular discrimination. Originality/value The results are new and never submitted before.