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 [5] 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.