Geodesic
Bounds for $f$-divergences under likelihood ratio constraints
Applications of Mathematics, Tome 48 (2003) no. 3, pp. 205-223.

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In this paper we establish an upper and a lower bound for the $f$-divergence of two discrete random variables under likelihood ratio constraints in terms of the Kullback-Leibler distance. Some particular cases for Hellinger and triangular discimination, $\chi ^2$-distance and Rényi’s divergences, etc. are also considered.
DOI : 10.1023/A:1026054413327
Classification : 26D15, 94A17
Keywords: $f$-divergence; divergence measures in information theory; Jensen’s inequality; Hellinger and triangular discrimination 
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Dragomir, S. S. Bounds for $f$-divergences under likelihood ratio constraints. Applications of Mathematics, Tome 48 (2003) no. 3, pp. 205-223. doi : 10.1023/A:1026054413327. http://geodesic.mathdoc.fr/articles/10.1023/A:1026054413327/

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