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

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. © 2020, The Author(s).

Authors
Siddique N.1 , Imran M.1 , Khan K.A.2 , Pečarić J. 3
Publisher
Springer International Publishing
Number of issue
1
Language
English
Status
Published
Number
430
Volume
2020
Year
2020
Organizations
  • 1 Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan
  • 2 Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan
  • 3 Rudn University, Moscow, Russian Federation
Keywords
Csiszár f-divergence; Fuchs’s theorem; Kullback–Leibler divergence; Majorization inequality; Montgomery identity; New Green’s functions; Shannon entropy; Čebyšev functional
Date of creation
02.11.2020
Date of change
02.11.2020
Short link
https://repository.rudn.ru/en/records/article/record/64299/
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