Sherman’s and related inequalities with applications in information theory
| Autor: | Naveed Latif, Ðilda Pečarić, Josip Pečarić, S. Ivelić Bradanović |
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| Rok vydání: | 2018 |
| Předmět: |
Zipf–Mandelbrot law
Information theory Inequality Sherman theorem Majorization inequality Jensen inequality Green Entropy media_common.quotation_subject 01 natural sciences Green function Discrete Mathematics and Combinatorics Entropy (information theory) 0101 mathematics 26D20 Mathematics Karamata's inequality media_common n-convex function Abel–Gontscharoff interpolating polynomial lcsh:Mathematics Research Applied Mathematics 010102 general mathematics 94A17 lcsh:QA1-939 010101 applied mathematics 26D15 Probability distribution ϕ-divergence Convex function Mathematical economics Jensen's inequality Analysis 26D99 |
| Zdroj: | Journal of Inequalities and Applications Journal of Inequalities and Applications, Vol 2018, Iss 1, Pp 1-21 (2018) |
| ISSN: | 1029-242X |
| Popis: | In this paper we give extensions of Sherman’s inequality considering the class of convex functions of higher order. As particular cases, we get an extended weighted majorization inequality as well as Jensen’s inequality which have direct connection to information theory. We use the obtained results to derive new estimates for Shannon’s and Rényi’s entropy, information energy, and some well-known measures between probability distributions. Using the Zipf–Mandelbrot law, we introduce new functionals to derive some related results. |
| Databáze: | OpenAIRE |
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