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

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

2005-01-19

arxiv.org/abs/math/0501302v1

Mathematics

Statistics Theory

This paper is a part of author's chapter to appear in 'Advances in Imaging and Electron Physics', 2005, Elsevier Publication

Scientific paper

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\'{a}r \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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