Probability in the Engineering and Informational Sciences.
Cambridge University Press.
2020.
A New Refinement of the Jensen Inequality with Applications in Information Theory
The Jensen inequality is one of the most important inequalities in theory of inequalities, and numerous results are devoted to this inequality. This inequality has many applications in several fields. This article is devoted to present a new interesting refinement of the well-known Jensen inequality and to give applications for means. The paper also aims to achieve numerous applications in information theory; in particular, a comprehensive detail has been given for Zipf’s law and obtained bounds for Zipf–Mandelbrot entropy. At the end of the article, a more general refinement of Jensen inequality is presented associated with m finite sequences. © 2020, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.
Authors
Khan M.A.1
,
Pečarić Ɖ.2
,
Pečarić J.
3
Publisher
Springer
Language
English
Status
Published
Link
Year
2020
Organizations
- 1 Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan
- 2 Catholic University of Croatia, Ilica 242, Zagreb, 10000, Croatia
- 3 RUDN University, Miklukho-Maklaya Str. 6, Moscow, 117198, Russian Federation
Keywords
Csiszár divergence; Jensen’s inequality; Means; Shannon entropy; Zipf–Mandelbrot entropy
Date of creation
02.11.2020
Date of change
02.11.2020
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Высшее образование в России.
Федеральное государственное бюджетное образовательное учреждение высшего образования "Московский политехнический университет".
Vol. 29.
2020.
P. 37-57