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On a Difference of Jensen Inequality and its Applications to Mean Divergence Measures

Inder Jeet Taneja
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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 Csiszár \cite{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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Inder Jeet Taneja. 2005-01-19. On a Difference of Jensen Inequality and its Applications to Mean Divergence Measures. https://arxiv.org/abs/math/0501302

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