Majorization inequalities via Green functions and Fink’s identity with applications to Shannon entropy

This paper is devoted to obtain generalized results related to majorization-type inequalities by using well-known Fink’s identity and new types of Green functions, introduced by Mehmood et al. (J. Inequal. Appl. 2017:108, 2017 ). We give a generalized majorization theorem for the class of n -convex functions. We utilize the Csiszár f -divergence and generalized majorization-type inequalities in providing the corresponding generalizations. As an application, we present the obtained results in terms of Shannon entropy and Kullback–Leibler distance.