NEW VERSIONS OF REVERSE YOUNG AND HEINZ MEAN INEQUALITIES WITH THE KANTOROVICH CONSTANT

Abstract

We show new versions of reverse Young inequalities by virtue of the Kantorovich constant, and utilizing the new reverse Young inequalities we give the reverses of the weighted arithmetic-geometric and geometric-harmonic mean inequalities for two positive operators. Also, new versions of reverse Young and Heinz mean inequalities for unitarily invariant norms are established.