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

Abstract

Abstract 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.

Keywords

• Majorization inequailty
• Fink’s identity
• New Green functions
• n-convex functions
• Čebyšev functional
• Csiszár f-divergence