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Series of New Information Divergences, Properties and Corresponding Series of Metric Spaces

K.C.Jain, Praphull Chhabra

Divergence measures are basically measures of distance between two probability distributions or these are useful for comparing two probability distributions. Depending on the nature of the problem, the different divergences are suitable. So it is always desirable to create a new divergence measure. There are several generalized functional divergences, such as: Csiszar divergence, Renyi- like divergence, Bregman divergence, Burbea- Rao divergence etc. all. In this paper, we obtain a series of divergences corresponding to a series of convex functions by using generalized Csiszar divergence. Further, we define the properties of convex functions and divergences, compare the divergences and lastly introduce the series of metric spaces.