On the power means and Lawson-Lim means for positive invertible operators

This note aims to present some reverse inequalities about the power means and Karcher mean via the Kantorovich constant and some of these have been generalized to higher power. Also, we generalize the reverse weighted arithmetic-geometric mean inequality of n positive invertible operators due to Lawson and Lim. In addition, we make comparisons between the Karcher mean and Lawson-Lim geometric mean for higher power.