A new refinement of Jensen’s inequality with applications in information theory

Author:

Xiao Lei1,Lu Guoxiang1

Affiliation:

1. School of Statistics and Mathematics, Zhongnan University of Economics and Law , Wuhan 430073 , P. R. China

Abstract

Abstract In this paper, we present a new refinement of Jensen’s inequality with applications in information theory. The refinement of Jensen’s inequality is obtained based on the general functional in the work of Popescu et al. As the applications in information theory, we provide new tighter bounds for Shannon’s entropy and some f-divergences.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference23 articles.

1. J. L. W. V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math. 30 (1906), no. 1, 175–193.

2. S. S. Dragomir, A refinement of Jensen’s inequality with applications for f-divergence measures, Taiwanese J. Math. 14 (2010), no. 1, 153–164.

3. S. S. Dragomir, A new refinement of Jensen’s inequality in linear spaces with applications, Math. Comput. Model. 52 (2010), 1497–1505.

4. P. G. Popescu, E. I. Slusanschi, V. Iancu, and F. Pop, A new upper bound for Shannon entropy. A novel approach in modeling of Big Data applications, Concurr. Comp.-Pract. Ex. 28 (2016), no. 2, 351–359.

5. L. Horvǎth, A method to refine the discrete Jensen’s inequality for convex and mid-convex functions, Math. Comput. Model. 54 (2011), 2451–2459.

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