Eine Bemerkung zu Verallgemeinerungen der Ungleichung vom arithmetischen und geometrischen Mittel

In the literature there are known homogeneous polynomialsP(x ₁,...,x _n) with real coefficients, for which (P(x_1 ,...,x_n ) leqslant P(bar x,...,bar x)) for allx _i≥0, and (bar x = (x_1 + ... + x_n )/n) . This paper gives two theorems, which lead to new polynomials of this kind.