The arithmetic-geometric-harmonic-mean and related matrix inequalities

Some More Inequalities for Arithmetic Mean, Harmonic Mean and Variance

We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality are obtained. Bounds for the largest and smallest eigenvalues of a positive definite matrix are also obtained.

Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

The matrix arithmetic-geometric mean inequality revisited

Interpolating between the Arithmetic-Geometric Mean and Cauchy-Schwarz matrix norm inequalities

We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.

A Note on the Weighted Harmonic–geometric–arithmetic Means Inequalities

In this note, we derive non trivial sharp bounds related to the weighted harmonicgeometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of a symmetric positive definite matrix and an inequality related to the coefficients of polynomials with positive roots. Mathematics subject classification (201...