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f -divergences play important role in probability theory, especially in information theory and in mathematical statistics. Remarkable divergences can be found among them. Inequalities for f -divergences are very useful and applicable in information theory. In this paper we give a precise equality condition and a refinement for one of the basic inequalities of f -divergences. The results are illustrated by some applications.

A refinement and an exact equality condition for the basic inequality of f-divergences