Abstract
AbstractIn 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.
Highlights
Introduction and PreliminariesZipf’s law [1,2,3] and the power laws in general [4,5,6] have and continue to attract considerable attention in a wide variety of disciplines from astronomy to demographics to software structure to economics to zoology, and even to warfare [7]
In this paper, we consider the de nition of "useful" Csiszár divergence and "useful" Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorization 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
Summary
Zipf’s law [1,2,3] and the power laws in general [4,5,6] have and continue to attract considerable attention in a wide variety of disciplines from astronomy to demographics to software structure to economics to zoology, and even to warfare [7]. The information conveyed by observing X is measured by the entropy which is de ned as (see [9, p.111])
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