Interpolating between the arithmetic-geometric mean and Cauchy-Schwarz matrix norm inequalities

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.

The matrix arithmetic-geometric mean inequality revisited

Inequalities related to the Cauchy-Schwarz inequality

We obtain an inequality complementary to the Cauchy-Schwarz inequality in Hilbert space. The inequalities involving first three powers of a self-adjoint operator are derived. The inequalities include the bounds for the third central moment, as a special case. It is shown that an upper bound for the spectral radius of a matrix is a root of a particular cubic equation, provided all eigenvalues ar...

Strengthened Cauchy-schwarz and Hölder Inequalities

We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of strengthened CauchySchwarz inequalities is derived using these identities. Also, an analogous version of this result is given for strengthened Hölder inequalities.

On Inequalities for Hypergeometric Analogues of the Arithmetic-geometric Mean

In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmetic-geometric mean established in [10].