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

Journal of inequalities and applications

article

Nouman Siddique¹  Muhammad Imran¹  Khuram Ali Khan²  Josip Pečarić³ 

[1] Department of Mathematics, Government College University;Department of Mathematics, University of Sargodha;Rudn University

关键词: Majorization inequailty;    Fink’s identity;    New Green functions;    n -convex functions;    Čebyšev functional;    Csiszár f -divergence;    Kullback–Leibler divergence;    Shannon entropy;   

DOI  :  10.1186/s13660-020-02455-0

学科分类：电力

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY