Sherman’s and related inequalities with applications in information theory

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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.

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Author and article information

Contributors

S. Ivelić Bradanović: sivelic@gradst.hr

N. Latif:

ORCID: http://orcid.org/0000-0002-9657-6711

naveed707@gmail.com

Ð. Pečarić: gildapeca@gmail.com

J. Pečarić: pecaric@element.hr

Journal

Journal ID (nlm-ta): J Inequal Appl

Journal ID (iso-abbrev): J Inequal Appl

Title: Journal of Inequalities and Applications

Publisher: Springer International Publishing (Cham )

ISSN (Print): 1025-5834

ISSN (Electronic): 1029-242X

Publication date (Electronic): 24 April 2018

Publication date PMC-release: 24 April 2018

Publication date (Print): 2018

Volume: 2018

Issue: 1

Electronic Location Identifier: 98

Affiliations

[1 ]ISNI 0000 0004 0644 1675, GRID grid.38603.3e, Faculty of Civil Engineering, Architecture And Geodesy, , University of Split, ; Split, Croatia

[2 ]ISNI 0000 0004 0607 924X, GRID grid.462426.0, Department of General Studies, , Jubail Industrial College, ; Jubail Industrial City, Kingdom of Saudi Arabia

[3 ]Catholic University of Croatia, Zagreb, Croatia

[4 ]ISNI 0000 0001 0657 4636, GRID grid.4808.4, Faculty of Textile Technology Zagreb, , University of Zagreb, ; Zagreb, Croatia

[5 ]ISNI 0000 0004 0645 517X, GRID grid.77642.30, RUDN University, ; Moscow, Russia

Author information

N. Latif http://orcid.org/0000-0002-9657-6711

Article

Publisher ID: 1692

DOI: 10.1186/s13660-018-1692-0

PMC ID: 5915592

SO-VID: 7b7d00e3-eafc-4e67-a64a-05e0fc440840

License:

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.