Majorization, "useful" Csiszár divergence and "useful" Zipf-Mandelbrot law

In this paper, we consider the definition of "useful" Csiszár divergence and "useful" Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorizatioQn inequalities by using monotonic sequences. We obtain the equivalent statements between continuous convex functions and Green functions via majorization inequalities, "useful" Csiszár functional and "useful" Zipf-Mandelbrot law. By considering "useful" Csiszár divergence in the integral case, we give the results for integral majorization inequality. Towards the end, some applications are given. © 2018 Latif et al., published by De Gruyter 2018.

Authors
Latif N.1 , Pečarić D.2 , Pečarić J. 3, 4
Journal
Open Mathematics
Publisher
De Gruyter
Number of issue
1
Language
English
Pages
1357-1373
Status
Published
Link
External link
DOI
10.1515/MATH-2018-0113
Volume
16
Year
2018
Organizations
  • 1 Department of General Studies, Jubail Industrial College, Jubail, Industrial City31961, Saudi Arabia
  • 2 Catholic University of Croatia, Ilica 242, Zagreb, 10000, Croatia
  • 3 Faculty of Textile Technology Zagreb, University of Zagreb, Prilaz Baruna Filipovića 28A, Zagreb, 10000, Croatia
  • 4 RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
Keywords
"Useful" Csiszár divergence, "Useful" Zipf-Mandelbrot law, Majorization inequality, Convex functions, Green functions, Information theory
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