A REVERSE INEQUALITY FOR THE WEIGHTED AM-GM INEQUALITY

Abstract

This paper presents a reverse inequality for the matrix version of the weighted Arithmetic Mean - Geometric Mean (AM-GM) inequality. More precisely, for t ∈ (0,1), 0 < mI_n ≤ A,B ≤ MI_n, where m, M are two positive real numbers, we prove that

where #_t, ∇_t are the weighted geometric mean and the weighted arithmetic mean, respectively, and h=M/m.