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+yaxb+yb)1a−bif a≠b,exp(xalogx+yalogyxa+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.