Sherman’s and related inequalities with applications in information theory

Autor:	S. Ivelić Bradanović, N. Latif, Ð. Pečarić, J. Pečarić
Jazyk:	angličtina
Rok vydání:	2018
Předmět:	Sherman theorem Majorization inequality Jensen inequality Green function Abel–Gontscharoff interpolating polynomial n-convex function Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2018, Iss 1, Pp 1-21 (2018)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-018-1692-0
Popis:	Abstract 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:	Directory of Open Access Journals
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