On a Difference of Jensen Inequality and its Applications to Mean Divergence Measures
Abstract
In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csisz\'ar csi1 f-divergence. A result is established that allow us to compare two measures under certain conditions. By the application of this result we have obtained a new inequality for the well known means such as arithmetic, geometric and harmonic. Some divergence measures based on these means are also defined.
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