Local monotonicity properties of two-variable Gini means and the comparison theorem revisited

In this paper we examine local monotonicity properties of the so-called Gini means, defined by Ga,b(x, y) =   xa + ya xb + yb 1 a−b if a = b, exp xa log x + ya log y xa + ya if a = b with respect to the parameters (a, b). As a consequence of our results, we obtain a new proof of the comparison theorem of two-variable Gini means.  2004 Elsevier Inc. All rights reserved.