A matrix inequality including that of Kantorov́ich

A Note on Matrix Versions of Kantorovich–type Inequality

Some new matrix versions of Kantorovich-Type inequalities for Hermitian matrix are proposed in this paper. We consider what happens to these inequalities when the positive definite matrix is allowed to be positive semidefinite singular or indefinite.

Several Matrix Euclidean Norm Inequalities Involving Kantorovich Inequality

where λ1 ≥ · · · ≥ λn > 0 are the eigenvalues of A. It is a very useful tool to study the inefficiency of the ordinary least-squares estimate with one regressor in the linear model. Watson 1 introduced the ratio of the variance of the best linear unbiased estimator to the variance of the ordinary least-squares estimator. Such a lower bound of this ratio was provided by Kantorovich inequality 1....

Generalization on Kantorovich Inequality

In this paper, we provide a new form of upper bound for the converse of Jensen’s inequality. Thereby, known estimations of the difference and ratio in Jensen’s inequality are essentially improved. As an application, we also obtain an improvement of Kantorovich inequality.

Improvements of Young inequality using the Kantorovich constant

‎Some improvements of Young inequality and its reverse for positive‎ ‎numbers with Kantorovich constant $K(t‎, ‎2)=frac{(1+t)^2}{4t}$‎ ‎are given‎. ‎Using these inequalities some operator inequalities and‎ ‎Hilbert-Schmidt norm versions for matrices are proved‎. ‎In‎ ‎particular‎, ‎it is shown that if $a‎, ‎b$ are positive numbers and‎ ‎$0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...

Refinements of Kantorovich Inequality for Hermitian Matrices