Refinement of Discrete Lah–Ribarič Inequality and Applications on Csiszár Divergence

Đilda Pečarić, Josip Pečarić and Jurica Perić
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Đilda Pečarić: Department of Media and Communication, University North, 48000 Koprivnica, Croatia
Josip Pečarić: Croatian Academy of Sciences and Arts, 10000 Zagreb, Croatia
Jurica Perić: Department of Mathematics, Faculty of Science, University of Split, 21000 Split, Croatia

Mathematics, 2022, vol. 10, issue 5, 1-18

Abstract: In this paper we give a new refinement of the Lah–Ribarič inequality and, using the same technique, we give a refinement of the Jensen inequality. Using these results, a refinement of the discrete Hölder inequality and a refinement of some inequalities for discrete weighted power means and discrete weighted quasi-arithmetic means are obtained. We also give applications in the information theory; namely, we give some interesting estimations for the discrete Csiszár divergence and for its important special cases.

Keywords: Lah–Ribari? inequality; Jensen inequality; Hölder’s inequalit; power mean; quasi-arithmetic mean; Csiszár divergence; Zipf–Mandelbrot law (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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