Schur-convexity and Schur-geometrically concavity of Gini means

The Schur-convexity and the Schur-geometric convexity with variables (x,y)∈R++2 for fixed (s,t)(s,t) of Gini means G(r,s;x,y)G(r,s;x,y) are discussed. Some new inequalities are obtained.