$f$ -Divergence Inequalities

Jensen-Ostrowski type inequalities and applications for f-divergence measures

In this paper, we provide inequalities of Jensen-Ostrowski type, by investigating the magnitude of the quantity ∫ Ω (f ◦ g) dμ− f(ζ)− ∫ Ω (g − ζ)f ′ ◦ g dμ+ 1 2 λ ∫ Ω (g − ζ) dμ, for various assumptions on the absolutely continuous function f : [a, b] → C, ζ ∈ [a, b], λ ∈ C and a μ-measurable function g on Ω. Special cases are considered to provide some inequalities of Jensen type, as well as O...

Mixed f - divergence and inequalities for log concave functions ∗

Mixed f -divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kull...

GEOMETRY OF f-DIVERGENCE*

Nested Inequalities Among Divergence Measures

In this paper we have considered an inequality having 11 divergence measures. Out of them three are logarithmic such as Jeffryes-Kullback-Leiber [4] [5] J-divergence. Burbea-Rao [1] Jensen-Shannon divergence and Taneja [7] arithmetic-geometric mean divergence. The other three are non-logarithmic such as Hellinger discrimination, symmetric χ−divergence, and triangular discrimination. Three more ...

Relative information of type s, Csiszár's f-divergence, and information inequalities

During past years Dragomir has contributed a lot of work providing different kinds of bounds on the distance, information and divergence measures. In this paper, we have unified some of his results using the relative information of type s and relating it with the Csisz ar’s f -divergence. 2003 Elsevier Inc. All rights reserved.