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

Abstract

Abstract 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.

Keywords

• Majorization inequality
• Fuchs’s theorem
• Montgomery identity
• New Green’s functions
• Čebyšev functional
• Csiszár f-divergence