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In this paper we give generalized results of a majorization inequality by using extension of the Montgomery identity and newly defined Green’s functions (Mehmood et al. in J. Inequal. Appl. 2017(1):108, 2017 ). We obtain a generalized majorization theorem for the class of n -convex functions. We use Csiszár f -divergence and generalized majorization-type inequalities to obtain new generalized results. We further discuss our obtained generalized results in terms of the Shannon entropy and the Kullback–Leibler distance.

Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy