The monotonicity and the Schur-convexity with parameters (s, t)
in R² for fixed (x, y) and the Schur-convexity and the Schur-geometrically
convexity with variables (x, y) in R²₊₊ for fixed (s, t) of Gini mean G(r, s; x, y)
are discussed. Some new inequalities are obtained.