Sequences of Inequalities Among Differences of Gini Means and Divergence Measures

In 1938, Gini [3] studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities arising due to particular values of each parameter of Gini’s mean. This sequence generates many nonnegative differences. Not all of them are convex. We have established new sequences of inequalities of these differences. Some refinement inequalities are also presented. Considering in terms of probability distributions these differences, we have made connections with some well known divergence measures.